Free Actions of Finite Groups on $S^n \times S^n$

Details Free Actions of Finite Groups on $S^n \times S^n$ Free Actions of Finite Groups on $S^n \times S^n$

2007-06-06

arxiv.org/abs/0706.0790v2

Mathematics

Algebraic Topology

Our preprint "Free actions of extraspecial p-groups on S^n x S^n" (arXiv:math/0701558) is now divided into two separate papers

Scientific paper

Let $p$ be an odd prime. We construct a non-abelian extension $\Gamma$ of $S^1$ by $Z/p \times Z/p$, 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 $p$ we obtain free smooth actions of infinitely many non-metacyclic rank two $p$-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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