{"paper":{"title":"Naturality of ${\\rm SL}_n$ quantum trace maps for surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hyun Kyu Kim, Zhihao Wang","submitted_at":"2024-12-22T10:39:49Z","abstract_excerpt":"The ${\\rm SL}_n$-skein algebra of a punctured surface $\\mathfrak{S}$, studied by Sikora, is an algebra generated by isotopy classes of $n$-webs living in the thickened surface $\\mathfrak{S} \\times (-1,1)$, where an $n$-web is a union of framed links and framed oriented $n$-valent graphs satisfying certain conditions. For each ideal triangulation $\\lambda$ of $\\mathfrak{S}$, L\\^e and Yu constructed an algebra homomorphism, called the ${\\rm SL}_n$-quantum trace, from the ${\\rm SL}_n$-skein algebra of $\\mathfrak{S}$ to a so-called balanced subalgebra of the $n$-root version of Fock and Goncharov'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16959","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/2412.16959/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"}