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
5 - Mayer–Vietoris Arguments and Further Properties of Intersection Homology
Published online by Cambridge University Press: 18 September 2020
- 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 develop “Mayer–Vietoris arguments” that can be used to show the equivalence of two functors on a manifold or stratified space. We apply such arguments to prove an intersection homology version of the Künneth theorem when one factor is a manifold; this includes a detailed construction of the cross product for intersection homology. We also treat intersection homology with coefficients and discuss universal coefficient theorems and their obstructions, including a local torsion-free condition. We show that PL and singular intersection homology are isomorphic on PL stratified spaces, and we prove that intersection homology is stratification-independent when using certain perversities, including the original ones of Goresky and MacPherson. The chapter closes with a proof that the intersection homology of compact pseudomanifolds is finitely generated.
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- Information
- Singular Intersection Homology , pp. 187 - 261Publisher: Cambridge University PressPrint publication year: 2020