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Free Actions of Finite Groups on Rational Homology 3-Spheres (1996)
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BibTeX
@MISC{Cooper96freeactions,
author = {D. Cooper and D. D. Long},
title = {Free Actions of Finite Groups on Rational Homology 3-Spheres},
year = {1996}
}
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Abstract
Introduction. The purpose of this note is to prove the following: Theorem 1.1 Let G be a finite group. Then there is a rational homology S 3 on which G acts freely. That any finite group acts freely on some closed 3-manifold is easy to arrange: There are many examples of closed 3-manifolds whose fundamental groups surject a free group of rank two (for example, by taking a connected sum of S 1 \Theta S 2 's) and by passing to a covering space, one can obtain a manifold whose group surjects a free group of any given rank. This gives a surjection onto any finite group and hence a free action on the associated covering space. We also note that results of Milnor [2] easily imply that one cannot replace rational coefficients by integral coefficients and hope for a similar result. The strategy for proving Theorem 1.1 is this: We begin with a free action of G<F
