Fixity and Free Group Actions on Products of Spheres

Details Fixity and Free Group Actions on Products of Spheres Fixity and Free Group Actions on Products of Spheres

2003-04-07

arxiv.org/abs/math/0304078v1

Mathematics

Algebraic Topology

22 pages

Scientific paper

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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