### 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 A_{5} on a 3-dimensional homology sphere having exactly one fixed point, where A_{5} is the alternating group on five letters.

Original language | English |
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Pages (from-to) | 191-220 |

Number of pages | 30 |

Journal | Publications of the Research Institute for Mathematical Sciences |

Volume | 37 |

Issue number | 2 |

Publication status | Published - 2001 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)