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.
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Masaharu Morimoto, <em>G</em>-surgery on 3-dimensional Manifolds for Homology Equivalences. Publ. Res. Inst. Math. Sci. 37 (2001), no. 2, pp. 191–220DOI 10.2977/PRIMS/1145476850