Fusion Systems and Constructing Free Actions on Products of Spheres

نویسنده

ÖZGÜN ÜNLÜ

چکیده

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×S1×· · ·×Sk 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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