Article ID Journal Published Year Pages File Type
4597770 Journal of Pure and Applied Algebra 2008 16 Pages PDF
Abstract

A finite group action on a lens space L(p,q)L(p,q) has ‘type OR’ if it reverses orientation and has an invariant Heegaard torus whose sides are interchanged by the orientation-reversing elements. In this paper we enumerate the actions of type OR up to equivalence. This leads to a complete classification of geometric finite group actions on amphicheiral lens spaces L(p,q)L(p,q) with p>2p>2. The family of actions of type OR is partially ordered by lifting actions via covering maps. We show that each connected component of this poset may be described in terms of a subset of the lattice of Gaussian integers ordered by divisibility. This results in a correspondence equating equivalence classes of actions of type OR with pairs of Gaussian integers.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, ,