{"paper":{"title":"Arithmetic quotients of the mapping class group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.GT","authors_text":"Alexander Lubotzky, Fritz Grunewald, Justin Malestein, Michael Larsen","submitted_at":"2013-07-09T20:44:32Z","abstract_excerpt":"To every $Q$-irreducible representation $r$ of a finite group $H$, there corresponds a simple factor $A$ of $Q[H]$ with an involution $\\tau$. To this pair $(A,\\tau)$, we associate an arithmetic group $\\Omega$ consisting of all $(2g-2)\\times (2g-2)$ matrices over a natural order of $A^{op}$ which preserve a natural skew-Hermitian sesquilinear form on $A^{2g-2}$. We show that if $H$ is generated by less than $g$ elements, then $\\Omega$ is a virtual quotient of the mapping class group $Mod(\\Sigma_g)$, i.e. a finite index subgroup of $\\Omega$ is a quotient of a finite index subgroup of $\\Mod(\\Sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2593","kind":"arxiv","version":2},"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"}