{"paper":{"title":"Entropy zero area preserving 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":"2010-02-01T19:56:01Z","abstract_excerpt":"In this paper we formulate and prove a structure theorem for area preserving diffeomorphisms of genus zero surfaces with zero entropy. As an application we relate the existence of faithful actions of a finite index subgroup of the mapping class group of a closed surface $\\Sigma_g$ on $S^2$ by area preserving diffeomorphisms to the existence of finite index subgroups of bounded mapping class groups $MCG(S, \\partial S)$ with non-trivial first cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0318","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"}