A characterisation of S^3 among homology spheres

Details A characterisation of S^3 among homology spheres A characterisation of S^3 among homology spheres

2006-06-09

arxiv.org/abs/math/0606220v2

Geom. Topol. Monogr. 14 (2008) 83-103

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 29 April 2008

Scientific paper

10.2140/gtm.2008.14.83

We prove that an integral homology 3-sphere is S^3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S^3. As an application we show that an irreducible integral homology sphere which is not S^3 is the cyclic branched cover of odd prime order of at most four knots in S^3. A result on the structure of finite groups of odd order acting on integral homology spheres is also obtained.

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