G-surgery on 3-dimensional Manifolds for Homology Equivalences

For a finite group G and a G-map f : X → Y of degree one, where X and Y 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...

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Bibliographic Details
Published inPublications of the Research Institute for Mathematical Sciences Vol. 37; no. 2; pp. 191 - 220
Main Author Morimoto, Masaharu
Format Journal Article
LanguageEnglish
Published Zuerich, Switzerland European Mathematical Society Publishing House 2001
Subjects
Manifolds and cell complexes
3-dimensional manifolds
Bak groups
3-dimensional homology spheres
equivariant surgery
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Summary:For a finite group G and a G-map f : X → Y of degree one, where X and Y 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.
ISSN:0034-5318
1663-4926
DOI:10.2977/prims/1145476850