Mathematics > Geometric Topology
[Submitted on 4 May 2014 (v1), last revised 22 Apr 2016 (this version, v3)]
Title:Free transformations of $S^1 \times S^n$ of square-free odd period
View PDFAbstract:Let $n$ be a positive integer, and let $\ell>1$ be square-free odd. We classify the set of equivariant homeomorphism classes of free $C_\ell$-actions on the product $S^1 \times S^n$ of spheres, up to indeterminacy bounded in $\ell$. 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 $\ell=2$ case was completed by B Jahren and S Kwasik (2011). The new issues for the case of $\ell$ odd are the presence of nontrivial ideal class groups and a group of equivariant self-equivalences with quadratic growth in $\ell$. The latter is handled by the composition formula for structure groups of A Ranicki (2009).
Submission history
From: Qayum Khan [view email][v1] Sun, 4 May 2014 13:53:14 UTC (25 KB)
[v2] Mon, 9 Feb 2015 05:27:02 UTC (26 KB)
[v3] Fri, 22 Apr 2016 21:58:10 UTC (28 KB)
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