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      Free actions of finite groups on Sn × Sn

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      Author
      Hambleton, Ian
      Ünlü, Özgün
      Date
      2010
      Source Title
      Transactions of the American Mathematical Society
      Print ISSN
      0002-9947
      Volume
      362
      Issue
      6
      Pages
      3289 - 3317
      Language
      English
      Type
      Article
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      Abstract
      Let p be an odd prime. We construct a non-abelian extension G of S 1 by Z/p × Z/p, and prove that any finite subgroup of G acts freely and smoothly on S2p-1 × S2p-1. In particular, for each odd prime p we obtain free smooth actions of infinitely many non-metacyclic rank two p-groups on S2p-1 × S2p-1. These results arise from a general approach to the existence problem for finite group actions on products of equidimensional spheres.
      Permalink
      http://hdl.handle.net/11693/22307
      Published Version (Please cite this version)
      http://dx.doi.org/10.1090/S0002-9947-09-05039-9
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      • Department of Mathematics 635
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