Fixity and Free Group Actions on Products of Spheres
Algebraic Topology
2007-05-23 v1 Geometric Topology
Abstract
We use the notion of fixity for representations of finite groups to construct free and smooth actions on products of spheres. In particular we show that a finite p-group (for p>3) will act freely and smoothly on a product of two spheres if and only if it does not contain a rank 3 elementary abelian subgroup. We show that if G is a finite subgroup of U(n), acting freely on U(n)/U(k) for some k>0 and if (|G|,(n-1)!)=1, then the action propagates to a free and smooth action on a product of n-k spheres. A number of explicit examples are discussed.
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Cite
@article{arxiv.math/0304078,
title = {Fixity and Free Group Actions on Products of Spheres},
author = {Alejandro Adem and James F. Davis and Ozgun Unlu},
journal= {arXiv preprint arXiv:math/0304078},
year = {2007}
}
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22 pages