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Qayum Khan (INDIANA): Free transformations of S^1 \times S^n of prime period (01/07/2014)


Let p be an odd prime, and let n be a positive integer. We classify the set of equivariant homeomorphism classes of free C_p-actions on the product S^1 \times S^n of spheres, up to indeterminacy bounded in p. The description is expressed in terms of number theory.

The techniques are various applications of surgery theory and homotopy theory, and we perform a careful study of h-cobordisms. The p=2 case was completed by B Jahren and S Kwasik (2011). The new issues for the odd p case are the presence of nontrivial ideal class groups and a group of equivariant self-equivalences with quadratic growth in p. The latter is handled by the composition formula for structure groups of A Ranicki (2009).

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