Singular Intersection Homology

The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.

Greg Friedman (Author)

9781107150744, Cambridge University Press

Hardback, published 24 September 2020

869 pages, 61 b/w illus.
17.5 x 25 x 5 cm, 1.5 kg

'… a detailed and meticulous presentation of intersection homology by singular and PL chains.' Daniel Tanré, European Mathematical Society

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.

Preface
Notations and conventions
1. Introduction
2. Stratified spaces
3. Intersection homology
4. Basic properties of singular and PL intersection homology
5. Mayer–Vietoris arguments and further properties of intersection homology
6. Non-GM intersection homology
7. Intersection cohomology and products
8. Poincaré duality
9. Witt spaces and IP spaces
10. Suggestions for further reading
Appendix A. Algebra
Appendix B. An introduction to simplicial and PL topology
References
Glossary of symbols
Index.

Subject Areas: Algebraic topology [PBPD], Algebra [PBF]