{"paper":{"title":"Galois actions on surfaces and a higher genus Grothendieck-Teichm\\\"uller group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.AT","authors_text":"Luciana Basualdo Bonatto, Marcy Robertson","submitted_at":"2026-05-31T21:55:13Z","abstract_excerpt":"We construct an operadic model for the higher-genus Teichm\\\"uller tower. More precisely, we define a modular operad $\\mathbf{S}$ in groupoids built from mapping class groups, with compositions and contractions encoding gluing operations on surfaces. We prove a presentation theorem for maps out of $\\mathbf{S}$, showing that they are determined by a small number of genus-zero and genus-one generators and relations. Using this presentation and the work of Nakamura--Schneps, we construct a faithful action of the Nakamura--Schneps subgroup $\\widehat{\\Gamma}\\subseteq\\widehat{\\mathsf{GT}}$ on the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01466","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01466/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"}