无平方奇周期的$S^1 \times S^n$的自由变换
Free transformations of $S^1 \times S^n$ of square-free odd period
摘要：
令$n$是正整数，并且令$\ell>1$是无平方的奇数。我们对球面积$S^1 \times S^n$上自由$C_\ell$ -作用的等变同胚类的集合进行了分类，直到不确定性在$\ell$中有界.描述是用数论来表达的。这些技术是手术理论和同伦理论的各种应用，我们进行了仔细的研究$h$ -协边。$\ell=2$病例由B Jahren和S Kwasik（2011）完成。$\ell$奇情形的新问题是$\ell$中存在非平凡理想类群和一组二次增长的等变自等价.后者由A Ranicki（2009）的结构群的组成公式处理。
英文摘要：
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).
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