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2 results

  • 9 - Witt Spaces and IP Spaces

  • Greg Friedman, Texas Christian University
  • Book:
    Singular Intersection Homology
    Published online:
    18 September 2020
    Print publication:
    24 September 2020, pp 613-702

  • 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.

Singular Intersection Homology
  • Greg Friedman
  • Published online:
    18 September 2020
    Print publication:
    24 September 2020
  • Intersection 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.