{"paper":{"title":"Free transformations of $S^1 \\times S^n$ of square-free odd period","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Qayum Khan","submitted_at":"2014-05-04T13:53:14Z","abstract_excerpt":"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.\n  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 equivari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0699","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}