Fusion systems and constructing free actions on products of spheres

Details Fusion systems and constructing free actions on products of spheres Fusion systems and constructing free actions on products of spheres

2010-06-30

arxiv.org/abs/1006.5797v1

Mathematics

Algebraic Topology

Scientific paper

We show that every rank two $p$-group acts freely and smoothly on a product of two spheres. This follows from a more general construction: given a smooth action of a finite group $G$ on a manifold $M$, we construct a smooth free action on $M \times \bbS ^{n_1} \times \dots \times \bbS ^{n_k}$ when the set of isotropy subgroups of the $G$-action on $M$ can be associated to a fusion system satisfying certain properties. Another consequence of this construction is that if $G$ is an (almost) extra-special $p$-group of rank $r$, then it acts freely and smoothly on a product of $r$ spheres.

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