{"paper":{"title":"Finite subgroups of Ham and Symp","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.SG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2016-05-18T09:33:49Z","abstract_excerpt":"Let $(X,\\omega)$ be a compact symplectic manifold of dimension $2n$ and let $Ham(X,\\omega)$ be its group of Hamiltonian diffeomorphisms. We prove the existence of a constant $C$, depending on $X$ but not on $\\omega$, such that any finite subgroup $G\\subset Ham(X,\\omega)$ has an abelian subgroup $A\\subseteq G$ satisfying $[G:A]\\leq C$, and $A$ can be generated by $n$ elements or fewer. If $b_1(X)=0$ we prove an analogous statement for the entire group of symplectomorphisms of $(X,\\omega)$. If $b_1(X)\\neq 0$ we prove the existence of a constant $C'$ depending only on $X$ such that any finite sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05494","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"}