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As an application we find that, for any prime $p\\geq 5$ a central extension of the genus $g$ mapping class group surjects onto the finite groups $\\mathbb G_p(\\Z/q\\Z)$, for all but finitely many primes $q$. This method provides infinitely many finite quotients of a given mapping class group out"},"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":"1106.4165","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-21T10:45:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"13928b3e9342a49da36fccf8cbc322976ad65cd177dd645b17fbc35398416ee0","abstract_canon_sha256":"1bf1793fa2324b1e92cfed5b4d7a1e84c01dbc068914c1c674f102dee330bbdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:35.492363Z","signature_b64":"IfmyGrTc4nFhCbZeNSq7kRq1ig/h1Eca3hlkZ1a1Hll2NvmZAh7x1D4iWramb0Ey8f2Z6NvhKmkESOYzorxuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc39b957c37d035e2e27eb76563f765e8d8bf24ef0fba5f16501a601e88f0fa3","last_reissued_at":"2026-05-18T01:17:35.491711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:35.491711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zariski density and finite quotients of mapping class groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Louis Funar","submitted_at":"2011-06-21T10:45:32Z","abstract_excerpt":"Our main result is that the image of the quantum representation of a central extension of the mapping class group of the genus $g\\geq 3$ closed orientable surface at a prime $p\\geq 5$ is a Zariski dense discrete subgroup of some higher rank algebraic semi-simple Lie group $\\mathbb G_p$ defined over $\\Q$. 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