{"paper":{"title":"Quotients of surface groups and homology of finite covers via quantum representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Ramanujan Santharoubane, Thomas Koberda","submitted_at":"2015-10-02T18:32:59Z","abstract_excerpt":"We prove that for each sufficiently complicated orientable surface $S$, there exists an infinite image linear representation $\\rho$ of $\\pi_1(S)$ such that if $\\gamma\\in\\pi_1(S)$ is freely homotopic to a simple closed curve on $S$, then $\\rho(\\gamma)$ has finite order. Furthermore, we prove that given a sufficiently complicated orientable surface $S$, there exists a regular finite cover $S'\\to S$ such that $H_1(S',\\mathbb{Z})$ is not generated by lifts of simple closed curves on $S$, and we give a lower bound estimate on the index of the subgroup generated by lifts of simple closed curves. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00677","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"}