{"paper":{"title":"Representations of surface groups with finite mapping class group orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Indranil Biswas, Mahan Mj, Ramanujan Santharoubane, Thomas Koberda","submitted_at":"2017-02-13T04:15:13Z","abstract_excerpt":"Let $(S,\\, \\ast)$ be a closed oriented surface with a marked point, let $G$ be a fixed group, and let $\\rho\\colon\\pi_1(S) \\longrightarrow G$ be a representation such that the orbit of $\\rho$ under the action of the mapping class group $Mod(S,\\, \\ast)$ is finite. We prove that the image of $\\rho$ is finite. A similar result holds if $\\pi_1(S)$ is replaced by the free group $F_n$ on $n\\geq 2$ generators and where $Mod(S,\\, \\ast)$ is replaced by $Aut(F_n)$. We thus resolve a well-known question of M. Kisin. We show that if $G$ is a linear algebraic group and if the representation variety of $\\pi_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03622","kind":"arxiv","version":1},"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"}