{"paper":{"title":"A compact symplectic four-manifold admits only finitely many inequivalent toric actions","license":"","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Liat Kessler, Martin Pinsonnault, Yael Karshon","submitted_at":"2006-09-01T21:26:12Z","abstract_excerpt":"Let (M,\\omega) be a four dimensional compact connected symplectic manifold. We prove that (M,\\omega) admits only finitely many inequivalent Hamiltonian effective 2-torus actions. Consequently, if M is simply connected, the number of conjugacy classes of 2-tori in the symplectomorphism group Sympl(M,\\omega) is finite. Our proof is \"soft\". The proof uses the fact that for symplectic blow-ups of \\CP^2 the restriction of the period map to the set of exceptional homology classes is proper. In an appendix, we describe results of McDuff that give a properness result for a general compact symplectic f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609043","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"}