A characterisation of S^3 among homology spheres

Michel Boileau; Luisa Paoluzzi; Bruno Zimmermann

doi:10.2140/gtm.2008.14.83

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A characterisation of S^3 among homology spheres

Michel Boileau·Luisa Paoluzzi·Bruno Zimmermann

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Abstract

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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Michel Boileau, Luisa Paoluzzi, Bruno Zimmermann. 2009-04-08. A characterisation of S^3 among homology spheres. https://doi.org/10.2140/gtm.2008.14.83

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