-surgery on 3-dimensional Manifolds for Homology Equivalences

  • Masaharu Morimoto

    Okayama University, Japan


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

Cite this article

Masaharu Morimoto, -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