{"paper":{"title":"Triviality of some representations of $MCG(S_g)$ in $GL(n,C), Diff(S^2)$ and $Homeo(T^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"John Franks, Michael Handel","submitted_at":"2011-02-22T19:20:59Z","abstract_excerpt":"We show the triviality of representations of the mapping class group of a genus $g$ surface in $GL(n,C), Diff(S^2)$ and $Homeo(T^2)$ when appropriate restrictions on the genus $g$ and the size of $n$ hold. For example, if $S_g$ is a surface of finite type and $\\phi : MCG(S_g) \\to GL(n,C)$ is a homomorphism, then $\\phi$ is trivial provided the genus $g \\ge 3$ and $n < 2g$. We also show that if $S_g$ is a closed surface with genus $g \\ge 7$, then every homomorphism $\\phi: MCG(S_g) \\to Diff(S^2)$ is trivial and that if $g \\ge 3$, then every homomorphism $\\phi: MCG(S_g) \\to Homeo(T^2)$ is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4584","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"}