Singular Intersection Homology
Singular Intersection Homology
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USDIntersection 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.
- Contains brand new research and results, bringing the reader right up to date
- Works as a reference for classical material, including detailed descriptions that are difficult to find elsewhere
- Provides a self-contained introduction to less standard background material, serving as a one-stop shop for the reader
Reviews & endorsements
'… a detailed and meticulous presentation of intersection homology by singular and PL chains.' Daniel Tanré, European Mathematical Society
'Overall, this monograph is a splendid introduction to noncommutative function-theoretic operator theory. Anyone interested in modern operator theory, function theory, and related areas of analysis will find this book a valuable reference.' Jaydeb Sarkar, MathSciNet
Product details
June 2025Hardback
9781107150744
869 pages
175 × 250 × 50 mm
1.5kg
61 b/w illus.
Not yet published - available from June 2025
Table of Contents
- 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.
