# <em>G</em>-surgery on 3-dimensional Manifolds for Homology Equivalences

### Masaharu Morimoto

Okayama University, Japan

## Abstract

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 _A_5 on a 3-dimensional homology sphere having exactly one fixed point, where _A_5 is the alternating group on five letters.

## Cite this article

Masaharu Morimoto, <em>G</em>-surgery on 3-dimensional Manifolds for Homology Equivalences. Publ. Res. Inst. Math. Sci. 37 (2001), no. 2, pp. 191–220

DOI 10.2977/PRIMS/1145476850