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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.4584","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-02-22T19:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"bb8c3daa449925a8a6a15d4b90406bfa46147e830e61c535b81d34209b451e2b","abstract_canon_sha256":"38c6a3c6a5e95534cefd0b97d787e74d2ef079fa9d93da9347059ea67560f99b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:45.193037Z","signature_b64":"W3185xe3srI+RNK2u1DR46wKm18xJP7miPE87Dme+0BtCSIDIMB4WEk9eVJOxnsFfQzPuW8ij3EmtCNO+AwfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ef117de605ca034be7c02df038a0553d471b52ad457eb932713e42d7b8bdae0","last_reissued_at":"2026-05-18T04:23:45.192340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:45.192340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $n < 2g$. 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