Fusion systems and constructing free actions on products of spheres

Ozgun Unlu; Ergun Yalcin

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arXiv · 1006.5797

Fusion systems and constructing free actions on products of spheres

Ozgun Unlu·Ergun Yalcin

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Abstract

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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BibTeX RIS

Ozgun Unlu, Ergun Yalcin. 2010-06-30. Fusion systems and constructing free actions on products of spheres. https://arxiv.org/abs/1006.5797

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