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- A characterisation of S^3 among homology spheres hal link

Auteur(s): Boileau Michel, Paoluzzi Luisa, Zimmermann Bruno

(Article) Publié: -Geom. Topol. Monogr., vol. 14 p.83-103 (2008)


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Résumé:

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.