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
9 - Witt Spaces and IP Spaces
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 Witt and IP spaces, which are the spaces on which middle-dimensional intersection cohomology self-pairings are possible. This leads to signature invariants for such spaces, and we demonstrate their basic properties, including Novikov additivity. Using the signature, we provide in detail the Goresky–MacPherson construction of the characteristic L-classes for Witt spaces, which is modeled upon the classical construction for PL manifolds. We also provide a survey of bordism groups and bordism homology theories based on different types of pseudomanifolds.
- Type
- Chapter
- Information
- Singular Intersection Homology , pp. 613 - 702Publisher: Cambridge University PressPrint publication year: 2020