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Fixity and Free Group Actions on Products of Spheres

Alejandro Adem·James F. Davis·Ozgun Unlu
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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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Alejandro Adem, James F. Davis, Ozgun Unlu. 2003-04-07. Fixity and Free Group Actions on Products of Spheres. https://arxiv.org/abs/math/0304078

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