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free actions on manifolds

Proceedings of the Edinburgh Mathematical Society (1)

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Fusion systems and group actions with abelian isotropy subgroups
Part of
- Representation theory of groups
Özgün Ünlü, Ergün Yalçin
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

10 July 2013, pp. 873-886
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We prove that if a finite group G acts smoothly on a manifold M such that all the isotropy subgroups are abelian groups with rank ≤ k, then G acts freely and smoothly on M × × … × for some positive integers n1, …, nk. We construct these actions using a recursive method, introduced in an earlier paper, that involves abstract fusion systems on finite groups. As another application of this method, we prove that every finite solvable group acts freely and smoothly on some product of spheres, with trivial action on homology.