{"paper":{"title":"Finite groups acting symplectically on $T^2\\times S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2015-02-09T10:31:17Z","abstract_excerpt":"For any symplectic form $\\omega$ on $T^2\\times S^2$ we construct infinitely many nonisomorphic finite groups which admit effective smooth actions on $T^2\\times S^2$ that are trivial in cohomology but which do not admit any effective symplectic action on $(T^2\\times S^2,\\omega)$. We also prove that for any $\\omega$ there is another symplectic form $\\omega'$ on $T^2\\times S^2$ and a finite group acting symplectically and effectively on $(T^2\\times S^2,\\omega')$ which does not admit any effective symplectic action on $(T^2\\times S^2,\\omega)$.\n  A basic ingredient in our arguments is the study of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02420","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"}