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Any finite group acts freely and homologically trivially on a product of spheres Davis, James


Suppose K is a finite CW complex with finite fundamental group G whose universal cover is homotopy equivalent to a product of spheres X. Suppose the G-action on the cover is trivial on homology. I will prove the following theorem using classical techniques from geometric topology. Theorem: G acts freely, smoothly, and homologically trivially on X x S^n whenever n is greater than or equal to the dimension of X. Unlu and Yalcin have constructed such a K for any finite fundamental group. Thus the title of the talk is a corollary.

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