{"paper":{"title":"Examples of Free Actions on Products of Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Ian Hambleton, Ozgun Unlu","submitted_at":"2007-05-28T17:51:54Z","abstract_excerpt":"We construct a non-abelian extension $\\Gamma$ of $S^1$ by $\\cy 3 \\times \\cy 3$, and prove that $\\Gamma$ acts freely and smoothly on $S^{5} \\times S^{5}$. This gives new actions on $S^{5} \\times S^{5}$ for an infinite family $\\cP$ of finite 3-groups. We also show that any finite odd order subgroup of the exceptional Lie group $G_2$ admits a free smooth action on $S^{11}\\times S^{11}$. This gives new actions on $S^{11}\\times S^{11}$ for an infinite family $\\cE $ of finite groups. We explain the significance of these families $\\cP $, $\\cE $ for the general existence problem, and correct some mist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4081","kind":"arxiv","version":2},"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"}