A characterisation of S3 among homology spheres
Abstract
We prove that an integral homology 3-sphere is S3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S3. As an application we show that an irreducible integral homology sphere which is not S3 is the cyclic branched cover of odd prime order of at most four knots in S3. A result on the structure of finite groups of odd order acting on integral homology spheres is also obtained.
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