On regular coverings of 3-manifolds by homology 3-spheres
Erhard Luft, Denis Sjerve · Pacific Journal of Mathematics · 1992
We study homology 3-spheres M that admit fixed point free actions by a finite group G.If G also admits a fixed point free orthogonal action on S 3 and if certain projective Z[ (7]-modules satisfy a cancellation property we show that the regular covering M -* M/G is induced from a standard regular covering S 3 -• S 3 /G by means of a map /: M/G -> S 3 /G whose degree is relatively prime to the order of G (Theorem 1).We also completely characterize those regular coverings M -• M where M is Seifert fibered ( §4).Finally, starting with any given regular covering M o -• Mo with group of covering transformations G, M o irreducible, and M o a homology 3-sphere, we show how to construct another regular covering M -• M with M a homology 3-sphere and the same group G of covering transformations, with M sufficiently large, M and M o not homotopy equivalent, and a degree 1 map /: Λf -• Mo that induces the regular covering M -• M from the regular covering MQ -> MQ .