G-surgery on 3-dimensional manifolds for homology equivalences

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Abstract

For a finite group G and a G-map f : X → Y of degree one, where X and F are compact, connected, oriented, 3-dimensional, smooth G-manifolds, we give an obstruction element σ(f) in a K-theoretic group called the Bak group, with the property: σ(f) = 0 guarantees that one can perform G-surgery on X so as to convert f to a homology equivalence f′ : X′ → Y. Using this obstruction theory, we determine the G-homeomorphism type of the singular set of a smooth action of A5 on a 3-dimensional homology sphere having exactly one fixed point, where A5 is the alternating group on five letters.

Original languageEnglish
Pages (from-to)191-220
Number of pages30
JournalPublications of the Research Institute for Mathematical Sciences
Volume37
Issue number2
Publication statusPublished - 2001

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Keywords

  • 3-dimensional homology spheres
  • 3-dimensional manifolds
  • Bak groups
  • Equivariant surgery

ASJC Scopus subject areas

  • Mathematics(all)

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