  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).
