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S_3 x S_3 acts freely on S^3 x S^3

James F. Davis
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Abstract

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a conjecture of Lewis made in 1968.

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James F. Davis. 1998-06-06. S_3 x S_3 acts freely on S^3 x S^3. https://arxiv.org/abs/math/9806027

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