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
8 - Poincaré Duality
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 show that oriented pseudomanifolds possess fundamental intersection homology classes, and we prove that intersection homology possesses a Poincaré duality given by the cap product with the fundamental class. We also prove Lefschetz duality for pseudomanifolds with boundary. We derive from both of these dualities nonsingular cup product and torsion pairings. We include an expositional survey of intersection pairings and the original approach of Goresky and MacPherson to intersection homology duality using such pairings.
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- Singular Intersection Homology , pp. 498 - 612Publisher: Cambridge University PressPrint publication year: 2020