{"paper":{"title":"Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"John Franks, Michael Handel","submitted_at":"2012-04-18T02:03:32Z","abstract_excerpt":"We show that if $M$ is a compact oriented surface of genus 0 and $G$ is a subgroup of $\\Symp^\\omega_\\mu(M)$ which has an infinite normal solvable subgroup, then $G$ is virtually abelian. In particular the centralizer of an infinite order $f \\in \\Symp^\\omega_\\mu(M)$ is virtually abelian. Another immediate corollary is that if $G$ is a solvable subgroup of $\\Symp^\\omega_\\mu(M)$ then $G$ is virtually abelian. We also prove a special case of the Tits Alternative for subgroups of $\\Symp^\\omega_\\mu(S^2).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3961","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"}