Geometry & Topology Monographs 14 (2008) 83–103

DOI: 10.2140/gtm.2008.14.83

arXiv: math/0606220

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.

Keywords

homology sphere, geometric structure, 3-manifold, cyclic branched covers, finite group action

Mathematical Subject Classification

Primary: 57M40

Secondary: 57M12, 57M50, 57M60, 57S17

References

Publication

Received: 8 June 2006
Accepted: 11 April 2007
Published: 29 April 2008

Authors