S₃ x S₃ acts freely on S³ x S³
classification
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math.AT
keywords
actionconstructedcopiesproductactscartesianconjecturecounterexample
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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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