Mathematics – Algebraic Topology
Scientific paper
2007-05-28
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
We construct a non-abelian extension $\Gamma$ of $S^1$ by $\cy 3 \times \cy 3$, and prove that $\Gamma$ acts freely and smoothly on $S^{5} \times S^{5}$. This gives new actions on $S^{5} \times S^{5}$ for an infinite family $\cP$ of finite 3-groups. We also show that any finite odd order subgroup of the exceptional Lie group $G_2$ admits a free smooth action on $S^{11}\times S^{11}$. This gives new actions on $S^{11}\times S^{11}$ for an infinite family $\cE $ of finite groups. We explain the significance of these families $\cP $, $\cE $ for the general existence problem, and correct some mistakes in the literature.
Hambleton Ian
Unlu Ozgun
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