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1 0 obj
<< /S /GoTo /D (chapter*.1) >>
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4 0 obj
(Preface)
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5 0 obj
<< /S /GoTo /D (chapter*.3) >>
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8 0 obj
(Notations and conventions)
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9 0 obj
<< /S /GoTo /D (chapter.1) >>
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12 0 obj
(Introduction)
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13 0 obj
<< /S /GoTo /D (section.1.1) >>
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16 0 obj
(What is intersection homology?)
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17 0 obj
<< /S /GoTo /D (section.1.2) >>
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20 0 obj
(Simplicial vs. PL vs. singular)
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21 0 obj
<< /S /GoTo /D (section.1.3) >>
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24 0 obj
(A note about sheaves and their scarcity here)
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25 0 obj
<< /S /GoTo /D (section.1.4) >>
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28 0 obj
(GM vs. non-GM intersection homology and an important note about notation)
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29 0 obj
<< /S /GoTo /D (section.1.5) >>
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32 0 obj
(Outline)
endobj
33 0 obj
<< /S /GoTo /D (chapter.2) >>
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36 0 obj
(Stratified Spaces)
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37 0 obj
<< /S /GoTo /D (section.2.1) >>
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40 0 obj
(First examples of stratified spaces)
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41 0 obj
<< /S /GoTo /D (section.2.2) >>
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44 0 obj
(Filtered and stratified spaces)
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45 0 obj
<< /S /GoTo /D (subsection.2.2.1) >>
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48 0 obj
(Filtered spaces)
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49 0 obj
<< /S /GoTo /D (subsection.2.2.2) >>
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52 0 obj
(Stratified spaces)
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53 0 obj
<< /S /GoTo /D (section*.5) >>
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56 0 obj
(Manifold stratified spaces)
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57 0 obj
<< /S /GoTo /D (subsection.2.2.3) >>
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60 0 obj
(Depth)
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61 0 obj
<< /S /GoTo /D (section.2.3) >>
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64 0 obj
(Locally conelike spaces and CS sets)
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65 0 obj
<< /S /GoTo /D (section.2.4) >>
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68 0 obj
(Pseudomanifolds)
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69 0 obj
<< /S /GoTo /D (section.2.5) >>
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72 0 obj
(PL spaces and PL pseudomanifolds)
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73 0 obj
<< /S /GoTo /D (subsection.2.5.1) >>
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76 0 obj
(PL spaces)
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77 0 obj
<< /S /GoTo /D (subsection.2.5.2) >>
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80 0 obj
(Piecewise linear and simplicial pseudomanifolds)
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81 0 obj
<< /S /GoTo /D (section*.6) >>
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84 0 obj
(Classical simplicial pseudomanifolds)
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85 0 obj
<< /S /GoTo /D (section.2.6) >>
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88 0 obj
(Normal pseudomanifolds)
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89 0 obj
<< /S /GoTo /D (section.2.7) >>
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92 0 obj
(Pseudomanifolds with boundaries)
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93 0 obj
<< /S /GoTo /D (section.2.8) >>
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96 0 obj
(Other species of stratified spaces)
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97 0 obj
<< /S /GoTo /D (subsection.2.8.1) >>
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100 0 obj
(Whitney stratified spaces)
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101 0 obj
<< /S /GoTo /D (subsection.2.8.2) >>
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104 0 obj
(Thom-Mather spaces)
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105 0 obj
<< /S /GoTo /D (subsection.2.8.3) >>
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108 0 obj
(Homotopically stratified spaces)
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109 0 obj
<< /S /GoTo /D (section.2.9) >>
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112 0 obj
(Maps of stratified spaces)
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113 0 obj
<< /S /GoTo /D (section.2.10) >>
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116 0 obj
(Advanced topic: intrinsic filtrations)
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117 0 obj
<< /S /GoTo /D (subsection.2.10.1) >>
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120 0 obj
(Intrinsic PL filtrations)
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121 0 obj
<< /S /GoTo /D (section*.7) >>
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124 0 obj
(Intrinsic filtrations of PL pseudomanifolds with boundary)
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125 0 obj
<< /S /GoTo /D (section.2.11) >>
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128 0 obj
(Advanced topic: products and joins)
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129 0 obj
<< /S /GoTo /D (subsection.2.11.1) >>
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132 0 obj
(Products of intrinsic filtrations)
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133 0 obj
<< /S /GoTo /D (chapter.3) >>
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136 0 obj
(Intersection homology)
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137 0 obj
<< /S /GoTo /D (section.3.1) >>
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140 0 obj
(Perversities)
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141 0 obj
<< /S /GoTo /D (subsection.3.1.1) >>
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144 0 obj
(GM perversities)
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145 0 obj
<< /S /GoTo /D (subsection.3.1.2) >>
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148 0 obj
(Dual perversities)
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149 0 obj
<< /S /GoTo /D (section.3.2) >>
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152 0 obj
(Simplicial intersection homology)
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153 0 obj
<< /S /GoTo /D (subsection.3.2.1) >>
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156 0 obj
(First examples)
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157 0 obj
<< /S /GoTo /D (section*.8) >>
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160 0 obj
(Allowability with respect to regular strata)
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161 0 obj
<< /S /GoTo /D (section*.9) >>
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164 0 obj
(Effects of subdivision)
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165 0 obj
<< /S /GoTo /D (section*.10) >>
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168 0 obj
(Some more advanced examples)
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169 0 obj
<< /S /GoTo /D (subsection.3.2.2) >>
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172 0 obj
(Some remarks on the definition)
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173 0 obj
<< /S /GoTo /D (section*.11) >>
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176 0 obj
(The motivation for the definition of intersection homology)
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177 0 obj
<< /S /GoTo /D (section*.12) >>
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180 0 obj
(Strata vs. skeleta in the definition of intersection chains)
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181 0 obj
<< /S /GoTo /D (section.3.3) >>
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184 0 obj
(PL intersection homology)
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185 0 obj
<< /S /GoTo /D (subsection.3.3.1) >>
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188 0 obj
(PL homology)
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189 0 obj
<< /S /GoTo /D (section*.13) >>
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192 0 obj
(PL chains and PL maps)
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193 0 obj
<< /S /GoTo /D (subsection.3.3.2) >>
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196 0 obj
(A useful alternative characterization of PL chains)
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197 0 obj
<< /S /GoTo /D (section*.14) >>
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200 0 obj
(Adding chains)
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201 0 obj
<< /S /GoTo /D (section*.15) >>
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204 0 obj
(Compatibility with PL maps)
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205 0 obj
<< /S /GoTo /D (section*.16) >>
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208 0 obj
(Realization)
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209 0 obj
<< /S /GoTo /D (subsection.3.3.3) >>
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212 0 obj
(PL intersection homology)
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213 0 obj
<< /S /GoTo /D (subsection.3.3.4) >>
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216 0 obj
(The relation between simplicial and PL intersection homology)
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217 0 obj
<< /S /GoTo /D (section.3.4) >>
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220 0 obj
(Singular intersection homology)
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221 0 obj
<< /S /GoTo /D (chapter.4) >>
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224 0 obj
(Basic properties of singular and PL intersection homology)
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225 0 obj
<< /S /GoTo /D (section.4.1) >>
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228 0 obj
(Stratified maps, homotopies, and homotopy equivalences)
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229 0 obj
<< /S /GoTo /D (section.4.2) >>
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232 0 obj
(The cone formula)
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233 0 obj
<< /S /GoTo /D (section.4.3) >>
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236 0 obj
(Relative intersection homology)
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237 0 obj
<< /S /GoTo /D (subsection.4.3.1) >>
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240 0 obj
(Further commentary on subspace filtrations)
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241 0 obj
<< /S /GoTo /D (subsection.4.3.2) >>
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244 0 obj
(Stratified maps revisited)
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245 0 obj
<< /S /GoTo /D (subsection.4.3.3) >>
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248 0 obj
(Reduced intersection homology and the relative cone formula)
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249 0 obj
<< /S /GoTo /D (section*.17) >>
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252 0 obj
(Reduced intersection homology)
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253 0 obj
<< /S /GoTo /D (section*.18) >>
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256 0 obj
(The relative cone formula)
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257 0 obj
<< /S /GoTo /D (section.4.4) >>
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260 0 obj
(Mayer-Vietoris sequences and excision)
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261 0 obj
<< /S /GoTo /D (subsection.4.4.1) >>
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264 0 obj
(PL excision and Mayer-Vietoris)
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265 0 obj
<< /S /GoTo /D (subsection.4.4.2) >>
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268 0 obj
(Singular subdivision, excision, and Mayer-Vietoris)
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269 0 obj
<< /S /GoTo /D (section*.19) >>
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272 0 obj
(Singular subdivision)
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273 0 obj
<< /S /GoTo /D (section*.24) >>
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276 0 obj
(Excision)
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277 0 obj
<< /S /GoTo /D (section*.25) >>
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280 0 obj
(Mayer-Vietoris)
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281 0 obj
<< /S /GoTo /D (section*.26) >>
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284 0 obj
(Examples)
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285 0 obj
<< /S /GoTo /D (section*.27) >>
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288 0 obj
(Relative Mayer-Vietoris sequences)
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289 0 obj
<< /S /GoTo /D (chapter.5) >>
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292 0 obj
(Mayer-Vietoris arguments and further properties of intersection homology)
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293 0 obj
<< /S /GoTo /D (section.5.1) >>
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296 0 obj
(Mayer-Vietoris arguments)
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297 0 obj
<< /S /GoTo /D (subsection.5.1.1) >>
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300 0 obj
(First applications: high perversities and normalization)
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301 0 obj
<< /S /GoTo /D (section*.28) >>
endobj
304 0 obj
(High perversities)
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305 0 obj
<< /S /GoTo /D (section*.29) >>
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308 0 obj
(Normalization)
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309 0 obj
<< /S /GoTo /D (section.5.2) >>
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312 0 obj
(Cross products and the K\374nneth theorem with a manifold factor)
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313 0 obj
<< /S /GoTo /D (subsection.5.2.1) >>
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316 0 obj
(The singular chain cross product)
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317 0 obj
<< /S /GoTo /D (subsection.5.2.2) >>
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320 0 obj
(The PL cross product)
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321 0 obj
<< /S /GoTo /D (subsection.5.2.3) >>
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324 0 obj
(Properties of the cross product)
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325 0 obj
<< /S /GoTo /D (subsection.5.2.4) >>
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328 0 obj
(K\374nneth theorem when one factor is a manifold)
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329 0 obj
<< /S /GoTo /D (section.5.3) >>
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332 0 obj
(Intersection homology with coefficients and universal coefficient theorems)
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333 0 obj
<< /S /GoTo /D (subsection.5.3.1) >>
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336 0 obj
(Definitions of intersection homology with coefficients)
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337 0 obj
<< /S /GoTo /D (section*.30) >>
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340 0 obj
(Comparing the options)
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341 0 obj
<< /S /GoTo /D (section*.31) >>
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344 0 obj
(Basic properties of intersection homology with coefficients)
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345 0 obj
<< /S /GoTo /D (subsection.5.3.2) >>
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348 0 obj
(Universal coefficient theorems)
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349 0 obj
<< /S /GoTo /D (section.5.4) >>
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352 0 obj
(Equivalence of PL and singular intersection homology on PL CS sets)
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353 0 obj
<< /S /GoTo /D (subsection.5.4.1) >>
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356 0 obj
(Barycentric subdivisions and maps from PL chains to singular chains)
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357 0 obj
<< /S /GoTo /D (subsection.5.4.2) >>
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360 0 obj
(The isomorphism of PL and singular intersection homology)
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361 0 obj
<< /S /GoTo /D (section.5.5) >>
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364 0 obj
(Topological invariance)
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365 0 obj
<< /S /GoTo /D (subsection.5.5.1) >>
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368 0 obj
(What perversities work?)
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369 0 obj
<< /S /GoTo /D (subsection.5.5.2) >>
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372 0 obj
(The statement of the theorem and some corollaries)
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373 0 obj
<< /S /GoTo /D (subsection.5.5.3) >>
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376 0 obj
(Proof of topological invariance)
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377 0 obj
<< /S /GoTo /D (section.5.6) >>
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380 0 obj
(Finite generation)
endobj
381 0 obj
<< /S /GoTo /D (chapter.6) >>
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384 0 obj
(Non-GM intersection homology)
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385 0 obj
<< /S /GoTo /D (section.6.1) >>
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388 0 obj
(Motivation for non-GM intersection homology)
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389 0 obj
<< /S /GoTo /D (section.6.2) >>
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392 0 obj
(Definitions of non-GM intersection homology)
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393 0 obj
<< /S /GoTo /D (subsection.6.2.1) >>
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396 0 obj
(First definition of IH)
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397 0 obj
<< /S /GoTo /D (subsection.6.2.2) >>
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400 0 obj
(Second definition of IH)
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401 0 obj
<< /S /GoTo /D (subsection.6.2.3) >>
endobj
404 0 obj
(Third definition of IH)
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405 0 obj
<< /S /GoTo /D (subsection.6.2.4) >>
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408 0 obj
(Non-GM intersection homology below the top perversity)
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409 0 obj
<< /S /GoTo /D (subsection.6.2.5) >>
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412 0 obj
(A new cone formula)
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413 0 obj
<< /S /GoTo /D (subsection.6.2.6) >>
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416 0 obj
(Relative non-GM intersection homology and the relative cone formula)
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417 0 obj
<< /S /GoTo /D (section.6.3) >>
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420 0 obj
(Properties of IH\(X;G\))
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421 0 obj
<< /S /GoTo /D (subsection.6.3.1) >>
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424 0 obj
(Basic properties)
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425 0 obj
<< /S /GoTo /D (section*.36) >>
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428 0 obj
(Maps and homotopies)
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429 0 obj
<< /S /GoTo /D (section*.37) >>
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432 0 obj
(Subdivision, excision, and Mayer-Vietoris)
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433 0 obj
<< /S /GoTo /D (section*.38) >>
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436 0 obj
(Applications of Mayer-Vietoris arguments)
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437 0 obj
<< /S /GoTo /D (section*.39) >>
endobj
440 0 obj
(Cross products)
endobj
441 0 obj
<< /S /GoTo /D (section*.40) >>
endobj
444 0 obj
(Coefficients)
endobj
445 0 obj
<< /S /GoTo /D (section*.41) >>
endobj
448 0 obj
(Agreement of singular and PL intersection homology)
endobj
449 0 obj
<< /S /GoTo /D (section*.42) >>
endobj
452 0 obj
(Finite generation)
endobj
453 0 obj
<< /S /GoTo /D (subsection.6.3.2) >>
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456 0 obj
(Dimensional homogeneity)
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457 0 obj
<< /S /GoTo /D (subsection.6.3.3) >>
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460 0 obj
(Local coefficients)
endobj
461 0 obj
<< /S /GoTo /D (section.6.4) >>
endobj
464 0 obj
(A general K\374nneth theorem)
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465 0 obj
<< /S /GoTo /D (subsection.6.4.1) >>
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468 0 obj
(A key example: the product of cones)
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469 0 obj
<< /S /GoTo /D (subsection.6.4.2) >>
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472 0 obj
(The K\374nneth Theorem)
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473 0 obj
<< /S /GoTo /D (subsection.6.4.3) >>
endobj
476 0 obj
(A relative K\374nneth theorem)
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477 0 obj
<< /S /GoTo /D (subsection.6.4.4) >>
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480 0 obj
(Applications of the K\374nneth Theorem)
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481 0 obj
<< /S /GoTo /D (subsection.6.4.5) >>
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484 0 obj
(Some technical stuff: the proof of Lemma 6.4.2)
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485 0 obj
<< /S /GoTo /D (section*.46) >>
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488 0 obj
(Algebra of the algebraic K\374nneth theorem)
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489 0 obj
<< /S /GoTo /D (section*.49) >>
endobj
492 0 obj
(Splitting)
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493 0 obj
<< /S /GoTo /D (section*.50) >>
endobj
496 0 obj
(Intersection homology products with cones)
endobj
497 0 obj
<< /S /GoTo /D (section.6.5) >>
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500 0 obj
(Advanced topic: chain splitting)
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501 0 obj
<< /S /GoTo /D (chapter.7) >>
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504 0 obj
(Intersection cohomology and products)
endobj
505 0 obj
<< /S /GoTo /D (section.7.1) >>
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508 0 obj
(Intersection cohomology)
endobj
509 0 obj
<< /S /GoTo /D (section.7.2) >>
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512 0 obj
(Cup, cap, and cross products)
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513 0 obj
<< /S /GoTo /D (subsection.7.2.1) >>
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516 0 obj
(Philosophy)
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517 0 obj
<< /S /GoTo /D (subsection.7.2.2) >>
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520 0 obj
(Intersection homology cup, cap, and cross products)
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521 0 obj
<< /S /GoTo /D (section*.51) >>
endobj
524 0 obj
(Hom of tensor products)
endobj
525 0 obj
<< /S /GoTo /D (section*.52) >>
endobj
528 0 obj
(Intersection Alexander-Whitney maps)
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529 0 obj
<< /S /GoTo /D (section*.53) >>
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532 0 obj
(The diagonal map)
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533 0 obj
<< /S /GoTo /D (section*.55) >>
endobj
536 0 obj
(The intersection cup, cap, and cross products)
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537 0 obj
<< /S /GoTo /D (section.7.3) >>
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540 0 obj
(Properties of cup, cap, and cross products. )
endobj
541 0 obj
<< /S /GoTo /D (subsection.7.3.1) >>
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544 0 obj
(Naturality)
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545 0 obj
<< /S /GoTo /D (section*.60) >>
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548 0 obj
(Naturality of the cross product)
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549 0 obj
<< /S /GoTo /D (section*.62) >>
endobj
552 0 obj
(Naturality of cup and cap products)
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553 0 obj
<< /S /GoTo /D (section*.65) >>
endobj
556 0 obj
(Compatibility with classical products)
endobj
557 0 obj
<< /S /GoTo /D (section*.66) >>
endobj
560 0 obj
(Topological invariance)
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561 0 obj
<< /S /GoTo /D (subsection.7.3.2) >>
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564 0 obj
(Commutativity)
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565 0 obj
<< /S /GoTo /D (subsection.7.3.3) >>
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568 0 obj
(Unitality and evaluation)
endobj
569 0 obj
<< /S /GoTo /D (section*.69) >>
endobj
572 0 obj
(Projection maps)
endobj
573 0 obj
<< /S /GoTo /D (section*.70) >>
endobj
576 0 obj
(Unital properties of products)
endobj
577 0 obj
<< /S /GoTo /D (section*.73) >>
endobj
580 0 obj
(Products and evaluations)
endobj
581 0 obj
<< /S /GoTo /D (subsection.7.3.4) >>
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584 0 obj
(Associativity)
endobj
585 0 obj
<< /S /GoTo /D (section*.74) >>
endobj
588 0 obj
(Associativity under broad assumptions)
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589 0 obj
<< /S /GoTo /D (section*.77) >>
endobj
592 0 obj
(Associativity in some more specific settings)
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593 0 obj
<< /S /GoTo /D (subsection.7.3.5) >>
endobj
596 0 obj
(Stability)
endobj
597 0 obj
<< /S /GoTo /D (section*.78) >>
endobj
600 0 obj
(Stability of cap products)
endobj
601 0 obj
<< /S /GoTo /D (section*.81) >>
endobj
604 0 obj
(Algebra of shifts and mapping cones )
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605 0 obj
<< /S /GoTo /D (section*.84) >>
endobj
608 0 obj
(Stability of cross products and cup products )
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609 0 obj
<< /S /GoTo /D (subsection.7.3.6) >>
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612 0 obj
(Criss-crosses)
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613 0 obj
<< /S /GoTo /D (section*.87) >>
endobj
616 0 obj
(The relation between cup and cross products)
endobj
617 0 obj
<< /S /GoTo /D (section*.88) >>
endobj
620 0 obj
(Interchange identities under broad assumptions)
endobj
621 0 obj
<< /S /GoTo /D (section*.91) >>
endobj
624 0 obj
(Interchange identities in some more specific settings)
endobj
625 0 obj
<< /S /GoTo /D (subsection.7.3.7) >>
endobj
628 0 obj
(Locality)
endobj
629 0 obj
<< /S /GoTo /D (subsection.7.3.8) >>
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632 0 obj
(The cohomology K\374nneth theorem)
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633 0 obj
<< /S /GoTo /D (subsection.7.3.9) >>
endobj
636 0 obj
(Summary of properties)
endobj
637 0 obj
<< /S /GoTo /D (subsection.7.3.10) >>
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640 0 obj
(Products on boundary-pseudomanifolds)
endobj
641 0 obj
<< /S /GoTo /D (section.7.4) >>
endobj
644 0 obj
(Intersection cohomology with compact supports)
endobj
645 0 obj
<< /S /GoTo /D (chapter.8) >>
endobj
648 0 obj
(Poincar\351 duality)
endobj
649 0 obj
<< /S /GoTo /D (section.8.1) >>
endobj
652 0 obj
(Orientations and fundamental classes)
endobj
653 0 obj
<< /S /GoTo /D (subsection.8.1.1) >>
endobj
656 0 obj
(Orientation and fundamental classes of manifolds)
endobj
657 0 obj
<< /S /GoTo /D (subsection.8.1.2) >>
endobj
660 0 obj
(Orientation of CS sets )
endobj
661 0 obj
<< /S /GoTo /D (subsection.8.1.3) >>
endobj
664 0 obj
(Homological properties of orientable pseudomanifolds)
endobj
665 0 obj
<< /S /GoTo /D (section*.95) >>
endobj
668 0 obj
(The orientation sheaf)
endobj
669 0 obj
<< /S /GoTo /D (section*.96) >>
endobj
672 0 obj
(Homological theorems)
endobj
673 0 obj
<< /S /GoTo /D (section*.101) >>
endobj
676 0 obj
(Useful corollaries)
endobj
677 0 obj
<< /S /GoTo /D (subsection.8.1.4) >>
endobj
680 0 obj
(Lack of global fundamental classes for subzero perversities)
endobj
681 0 obj
<< /S /GoTo /D (subsection.8.1.5) >>
endobj
684 0 obj
(Invariance of fundamental classes)
endobj
685 0 obj
<< /S /GoTo /D (section*.102) >>
endobj
688 0 obj
(Fundamental classes under change of perversity)
endobj
689 0 obj
<< /S /GoTo /D (section*.103) >>
endobj
692 0 obj
(Fundamental classes under change of stratification)
endobj
693 0 obj
<< /S /GoTo /D (subsection.8.1.6) >>
endobj
696 0 obj
(Intersection homology factors the cap product)
endobj
697 0 obj
<< /S /GoTo /D (section*.104) >>
endobj
700 0 obj
(More general factorizations)
endobj
701 0 obj
<< /S /GoTo /D (subsection.8.1.7) >>
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704 0 obj
(Product spaces)
endobj
705 0 obj
<< /S /GoTo /D (section.8.2) >>
endobj
708 0 obj
(Poincar\351 duality)
endobj
709 0 obj
<< /S /GoTo /D (subsection.8.2.1) >>
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712 0 obj
(The duality map)
endobj
713 0 obj
<< /S /GoTo /D (subsection.8.2.2) >>
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716 0 obj
(The Poincar\351 Duality Theorem)
endobj
717 0 obj
<< /S /GoTo /D (subsection.8.2.3) >>
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720 0 obj
(Duality of torsion free conditions)
endobj
721 0 obj
<< /S /GoTo /D (subsection.8.2.4) >>
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724 0 obj
(Topological invariance of Poincar\351 duality)
endobj
725 0 obj
<< /S /GoTo /D (section.8.3) >>
endobj
728 0 obj
(Lefschetz duality)
endobj
729 0 obj
<< /S /GoTo /D (subsection.8.3.1) >>
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732 0 obj
(Orientations and fundamental classes)
endobj
733 0 obj
<< /S /GoTo /D (section*.114) >>
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(Topological invariance)
endobj
737 0 obj
<< /S /GoTo /D (subsection.8.3.2) >>
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740 0 obj
(Lefschetz duality)
endobj
741 0 obj
<< /S /GoTo /D (section*.115) >>
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744 0 obj
(Topological invariance)
endobj
745 0 obj
<< /S /GoTo /D (section.8.4) >>
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748 0 obj
(The cup product and torsion pairings)
endobj
749 0 obj
<< /S /GoTo /D (subsection.8.4.1) >>
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752 0 obj
(Some algebra)
endobj
753 0 obj
<< /S /GoTo /D (section*.116) >>
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(Pairings)
endobj
757 0 obj
<< /S /GoTo /D (section*.117) >>
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760 0 obj
(Torsion submodules and torsion-free quotients)
endobj
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<< /S /GoTo /D (subsection.8.4.2) >>
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(The cup product pairing)
endobj
765 0 obj
<< /S /GoTo /D (subsection.8.4.3) >>
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768 0 obj
(The torsion pairing)
endobj
769 0 obj
<< /S /GoTo /D (section*.118) >>
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(The components of lambda)
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<< /S /GoTo /D (section*.119) >>
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(Assembling lambda)
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<< /S /GoTo /D (section*.120) >>
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780 0 obj
(The torsion pairing made explicit)
endobj
781 0 obj
<< /S /GoTo /D (section*.121) >>
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(Symmetry and nonsingularity)
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785 0 obj
<< /S /GoTo /D (section*.122) >>
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(Another approach to the torsion pairing)
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789 0 obj
<< /S /GoTo /D (subsection.8.4.4) >>
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(Topological invariance of pairings)
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<< /S /GoTo /D (subsection.8.4.5) >>
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(Image pairings)
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<< /S /GoTo /D (section*.123) >>
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(Nondegeneracy)
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<< /S /GoTo /D (section*.124) >>
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(The intersection cohomology image pairing)
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<< /S /GoTo /D (section.8.5) >>
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808 0 obj
(The Goresky-MacPherson intersection pairing)
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809 0 obj
<< /S /GoTo /D (subsection.8.5.1) >>
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812 0 obj
(The intersection pairing on manifolds)
endobj
813 0 obj
<< /S /GoTo /D (section*.125) >>
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816 0 obj
(What should the intersection product be?)
endobj
817 0 obj
<< /S /GoTo /D (section*.126) >>
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820 0 obj
(The PL intersection pairing)
endobj
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<< /S /GoTo /D (subsection.8.5.2) >>
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(The intersection pairing on PL pseudomanifolds)
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<< /S /GoTo /D (section*.128) >>
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(Almost full circle)
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<< /S /GoTo /D (subsection.8.5.3) >>
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(An intersection pairing on topological pseudomanifolds and some relations of Goresky and MacPherson)
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833 0 obj
<< /S /GoTo /D (chapter.9) >>
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(Witt spaces and IP spaces)
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837 0 obj
<< /S /GoTo /D (section.9.1) >>
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(Witt and IP spaces)
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841 0 obj
<< /S /GoTo /D (subsection.9.1.1) >>
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(Witt spaces)
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<< /S /GoTo /D (section*.129) >>
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(Dependence of Witt spaces on coefficient choices)
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<< /S /GoTo /D (subsection.9.1.2) >>
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(IP spaces)
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<< /S /GoTo /D (subsection.9.1.3) >>
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(Products and stratification independence)
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<< /S /GoTo /D (section.9.2) >>
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(Self pairings)
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<< /S /GoTo /D (section.9.3) >>
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(Witt signatures)
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<< /S /GoTo /D (subsection.9.3.1) >>
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(Definitions and basic properties)
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<< /S /GoTo /D (section*.132) >>
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(Signatures of matrices and pairings)
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<< /S /GoTo /D (section*.133) >>
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(Witt signatures)
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<< /S /GoTo /D (section*.135) >>
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(Topological invariance of Witt signatures)
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<< /S /GoTo /D (subsection.9.3.2) >>
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(Properties of Witt signatures)
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<< /S /GoTo /D (subsection.9.3.3) >>
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(Novikov additivity)
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<< /S /GoTo /D (subsection.9.3.4) >>
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(Perverse signatures)
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<< /S /GoTo /D (section.9.4) >>
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(L-classes)
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<< /S /GoTo /D (subsection.9.4.1) >>
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(Outline of the construction of L-classes \(without proofs\))
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<< /S /GoTo /D (section*.136) >>
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(Maps to spheres and embedded subspaces)
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<< /S /GoTo /D (section*.137) >>
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(Cohomotopy)
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<< /S /GoTo /D (section*.138) >>
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(The L-classes)
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<< /S /GoTo /D (section*.139) >>
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(L-classes on smooth manifolds)
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<< /S /GoTo /D (section*.140) >>
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<< /S /GoTo /D (section*.141) >>
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(Characterizing the L-classes)
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<< /S /GoTo /D (section*.145) >>
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(Some notation)
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<< /S /GoTo /D (section*.146) >>
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(The proofs)
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<< /S /GoTo /D (subsection.9.4.2) >>
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(Maps to spheres and embedded subspaces)
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<< /S /GoTo /D (subsection.9.4.3) >>
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(Cohomotopy)
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<< /S /GoTo /D (subsection.9.4.4) >>
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(The L-classes)
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<< /S /GoTo /D (subsection.9.4.5) >>
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(L-classes in small degrees)
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<< /S /GoTo /D (section*.154) >>
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(Extending properties to small degrees)
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<< /S /GoTo /D (subsection.9.4.6) >>
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(Characterizing the L-classes)
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<< /S /GoTo /D (section.9.5) >>
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(A survey of pseudomanifold bordism theories)
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<< /S /GoTo /D (subsection.9.5.1) >>
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(Bordism)
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<< /S /GoTo /D (section*.155) >>
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(Bordism groups)
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<< /S /GoTo /D (section*.156) >>
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(Bordism homology theories)
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<< /S /GoTo /D (subsection.9.5.2) >>
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(Pseudomanifold bordism)
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<< /S /GoTo /D (chapter.10) >>
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(Suggestions for further reading)
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<< /S /GoTo /D (section.10.1) >>
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(Background, foundations, and next texts)
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<< /S /GoTo /D (subsection.10.1.1) >>
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(Deeper background)
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<< /S /GoTo /D (section*.165) >>
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(Sheaf theory)
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<< /S /GoTo /D (section*.166) >>
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(Derived categories and Verdier duality)
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<< /S /GoTo /D (section.10.2) >>
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(Bordism)
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<< /S /GoTo /D (section.10.3) >>
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(Characteristic classes)
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<< /S /GoTo /D (section.10.4) >>
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(Intersection spaces)
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<< /S /GoTo /D (section.10.5) >>
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(Analytic approaches to intersection cohomology)
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<< /S /GoTo /D (subsection.10.5.1) >>
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(L2 cohomology)
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<< /S /GoTo /D (subsection.10.5.2) >>
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(Perverse forms)
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<< /S /GoTo /D (section*.167) >>
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(Chataur-Saralegi-Tanr\351 theory)
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1025 0 obj
<< /S /GoTo /D (section.10.6) >>
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(Stratified Morse Theory)
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<< /S /GoTo /D (section.10.7) >>
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(Perverse sheaves and the Decomposition Theorem)
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<< /S /GoTo /D (section.10.8) >>
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(Hodge theory)
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1037 0 obj
<< /S /GoTo /D (section.10.9) >>
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(Miscellaneous)
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<< /S /GoTo /D (appendix.A) >>
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(Algebra)
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<< /S /GoTo /D (section.A.1) >>
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(Koszul sign conventions)
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<< /S /GoTo /D (subsection.A.1.1) >>
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(Why sign?)
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<< /S /GoTo /D (subsection.A.1.2) >>
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(Homological versus cohomological grading)
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<< /S /GoTo /D (subsection.A.1.3) >>
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(The chain complex of maps of chain complexes)
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<< /S /GoTo /D (subsection.A.1.4) >>
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(Chain maps and chain homotopies)
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<< /S /GoTo /D (subsection.A.1.5) >>
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(Consequences)
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<< /S /GoTo /D (section.A.2) >>
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(Some more facts about chain homotopies)
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<< /S /GoTo /D (section.A.3) >>
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(Shifts and mapping cones)
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<< /S /GoTo /D (subsection.A.3.1) >>
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(Shifts)
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<< /S /GoTo /D (subsection.A.3.2) >>
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(Algebraic mapping cones)
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<< /S /GoTo /D (section.A.4) >>
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(Projective modules and Dedekind domains)
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<< /S /GoTo /D (subsection.A.4.1) >>
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(Projective modules)
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<< /S /GoTo /D (subsection.A.4.2) >>
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(Dedekind domains)
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<< /S /GoTo /D (section.A.5) >>
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(Linear algebra of signatures)
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<< /S /GoTo /D (appendix.B) >>
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(An introduction to simplicial and PL topology)
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<< /S /GoTo /D (section.B.1) >>
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(Simplicial complexes and Euclidean polyhedra)
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1109 0 obj
<< /S /GoTo /D (subsection.B.1.1) >>
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(Simplicial complexes)
endobj
1113 0 obj
<< /S /GoTo /D (subsection.B.1.2) >>
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(Euclidean polyhedra)
endobj
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<< /S /GoTo /D (section.B.2) >>
endobj
1120 0 obj
(PL spaces and PL maps)
endobj
1121 0 obj
<< /S /GoTo /D (section.B.3) >>
endobj
1124 0 obj
(Comparing our two notions of PL spaces)
endobj
1125 0 obj
<< /S /GoTo /D (section.B.4) >>
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1128 0 obj
(PL subspaces)
endobj
1129 0 obj
<< /S /GoTo /D (section.B.5) >>
endobj
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(Cones, joins, and products of PL spaces)
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1133 0 obj
<< /S /GoTo /D (section.B.6) >>
endobj
1136 0 obj
(The Eilenberg-Zilber shuffle triangulation of products)
endobj
1137 0 obj
<< /S /GoTo /D (subsection.B.6.1) >>
endobj
1140 0 obj
(The definition of the Eilenberg-Zilber triangulation)
endobj
1141 0 obj
<< /S /GoTo /D (subsection.B.6.2) >>
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1144 0 obj
(Realization of partially ordered sets)
endobj
1145 0 obj
<< /S /GoTo /D (subsection.B.6.3) >>
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(Products of partially ordered sets and their product triangulations)
endobj
1149 0 obj
<< /S /GoTo /D (subsection.B.6.4) >>
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1152 0 obj
(Triangulations of products of simplicial complexes and PL spaces)
endobj
1153 0 obj
<< /S /GoTo /D (subsection.B.6.5) >>
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1156 0 obj
(The simplicial cross product)
endobj
1157 0 obj
<< /S /GoTo /D (section*.173) >>
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1160 0 obj
(Bibliography)
endobj
1161 0 obj
<< /S /GoTo /D (section*.175) >>
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(Index)
endobj
1165 0 obj
<< /S /GoTo /D (section*.176) >>
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(Glossary of symbols)
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<< /S /GoTo /D [1170 0 R /Fit] >>
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