English

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