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      Fusion systems and constructing free actions on products of spheres

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      Author
      Ünlü, Ö.
      Yalçın, E.
      Date
      2012
      Source Title
      Mathematische Zeitschrift
      Print ISSN
      0025-5874
      Electronic ISSN
      1432-1823
      Publisher
      Springer
      Volume
      270
      Issue
      3-4
      Pages
      939 - 959
      Language
      English
      Type
      Article
      Item Usage Stats
      131
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      98
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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 × S n1× ... × S nk 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. © 2011 Springer-Verlag.
      Keywords
      Primary 57S25
      Secondary 20D20
      Permalink
      http://hdl.handle.net/11693/21529
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s00209-010-0833-z
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