{"paper":{"title":"Power quotients of surface groups and mapping class groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Alessandro Sisto, Henry Wilton, R\\'emi Coulon","submitted_at":"2025-07-18T07:10:21Z","abstract_excerpt":"Let $\\Gamma$ be the fundamental group of a closed, orientable, hyperbolic surface $S$. The $n$-power quotient, $\\Gamma(n)$, is the quotient of $\\Gamma$ by the $n$th powers of simple closed curves. We prove an analogue of the Dehn--Nielsen--Baer theorem for suitable large values of $n$: the outer automorphism group of $\\Gamma(n)$ is isomorphic to the quotient of the extended mapping class group of $S$ by $n$th powers of Dehn twists. There is also a corresponding description of the automorphism group as the quotient of the extended mapping class group of the corresponding once-punctured surface,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13701","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.13701/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}