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Intersection Cohomology, Simplicial Blow-Up and Rational Homotopy(MEMO/254/1214) P 108 p. 18
Chataur, David,
Saralegi-Aranguren, Martintxo,
Tanre, Daniel
著
発行年月 |
2018年08月 |
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出版国 |
アメリカ合衆国 |
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言語 |
英語 |
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媒体 |
冊子 |
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装丁 |
paper |
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ページ数/巻数 |
108 p. |
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ジャンル |
洋書/理工学/数学/代数学 |
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ISBN |
9781470428877 |
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商品コード |
1027483733 |
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本の性格 |
学術書 |
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新刊案内掲載月 |
2018年07月 |
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商品URL
| https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=1027483733 |
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内容
Let $X$ be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of $X$, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when $X$ is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field $\mathbb Q$. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.