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ISSN 1088-6850(e) ISSN 0002-9947(p)

Free actions of finite groups on $S^n \times S^n$

Author(s): Ian Hambleton; Özgün Ünlü
Journal: Trans. Amer. Math. Soc. 362 (2010), 3289-3317.
MSC (2010): Primary 57S17, 57R67
Posted: December 15, 2009
MathSciNet review: 2592957
Retrieve article in: PDF

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Abstract: Let be an odd prime. We construct a non-abelian extension $\Gamma$ of by $\mathbf{Z}/p \times \mathbf{Z}/p$ , and prove that any finite subgroup of $\Gamma$ acts freely and smoothly on $S^{2p-1} \times S^{2p-1}$ . In particular, for each odd prime we obtain free smooth actions of infinitely many non-metacyclic rank two -groups on $S^{2p-1} \times S^{2p-1}$ . These results arise from a general approach to the existence problem for finite group actions on products of equidimensional spheres.

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