Singular Intersection Homology

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Cambridge University Press, Sep 24, 2020 - Mathematics - 869 pages
Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.
 

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Contents

Introduction
1
Stratified Spaces
16
Intersection Homology
86
Basic Properties of Singular and PL Intersection Homology
135
MayerVietoris Arguments and Further Properties of Intersection
187
6
262
Poincaré Duality
498
Witt Spaces and IP Spaces
613
Suggestions for Further Reading
703
AppendixA Algebra
713
Appendix B An Introduction to Simplicial and PL Topology
739
References
769
Glossary of Symbols
781
Index
787
7
794
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About the author (2020)

Greg Friedman is Professor of Mathematics at Texas Christian University. Professor Friedman's primary research is in geometric and algebraic topology with particular emphases on stratified spaces and high-dimensional knot theory. He has given introductory lecture series on intersection homology at the University of Lille and the Fields Institute for Research in Mathematical Sciences. He has received grants from the National Science Foundation and the Simons Foundation.

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