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1 results

  • 5 - Mayer–Vietoris Arguments and Further Properties of Intersection Homology

  • Greg Friedman, Texas Christian University
  • Book:
    Singular Intersection Homology
    Published online:
    18 September 2020
    Print publication:
    24 September 2020, pp 187-261

  • 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.