A characterisation of S^3 among homology spheres
Geometric Topology
2009-04-08 v2
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.
Keywords
Cite
@article{arxiv.math/0606220,
title = {A characterisation of S^3 among homology spheres},
author = {Michel Boileau and Luisa Paoluzzi and Bruno Zimmermann},
journal= {arXiv preprint arXiv:math/0606220},
year = {2009}
}
Comments
This is the version published by Geometry & Topology Monographs on 29 April 2008