{"paper":{"title":"Free and properly discontinuous actions of groups on homotopy $2n$-spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daciberg Lima Goncalves, Marek Golasinski, Rolando Jimenez","submitted_at":"2014-02-01T20:55:15Z","abstract_excerpt":"Let $G$ be a group acting freely, properly discontinuously and cellularly on a finite dimensional $C$W-complex $\\Sigma(2n)$ which has the homotopy type of the $2n$- sphere $\\mathbb{S}^{2n}$. Then, this action induces an action of the group $G$ on the top cohomology of $\\Sigma(2n)$. For the family of virtually cyclic groups, we classify all groups which act on $\\Sigma(2n)$, the homotopy type of all possible orbit spaces and all actions on the top cohomology as well. \\par Under the hypothesis that $\\mbox{dim}\\,\\Sigma(2n)\\leq 2n+1$, we study the groups with the virtual cohomological dimension $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0124","kind":"arxiv","version":1},"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"}