Intersection cohomology, simplicial blow-up and rational homotopy
Author(s)
Bibliographic Information
Intersection cohomology, simplicial blow-up and rational homotopy
（Memoirs of the American Mathematical Society, no. 1214）
American Mathematical Society, c2018
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"Volume 254, number 1214 (second of 5 numbers), July 2018"
Includes bibliographical references (p. 103-105) and index
Description and Table of Contents
Description
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.
Table of Contents
- Introduction
- Simplicial blow-up
- Rational algebraic models
- Formality and examples
- Appendix A. Topological setting
- Bibliography
- Index.
by "Nielsen BookData"