Book contents
- Frontmatter
- Dedication
- 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
6 - Non-GM Intersection Homology
Published online by Cambridge University Press: 18 September 2020
Book contents
- Frontmatter
- Dedication
- 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
Summary
We introduce “non-GM” intersection homology, which is a version of intersection homology that has better properties for arbitrary perversity parameters, though it agrees with GM intersection homology with certain perversity restrictions. We develop the basic properties of this version of intersection homology, including behavior under stratified maps and homotopies, relative intersection homology, excision, Mayer–Vietoris sequences, cross products, and a new cone formula. We also develop a Künneth theorem for products of stratified spaces, and prove theorems about splitting intersection chains into smaller pieces.
Keywords
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- Information
- Singular Intersection Homology , pp. 262 - 352Publisher: Cambridge University PressPrint publication year: 2020