{"paper":{"title":"Naturality of ${\\rm SL}_3$ quantum trace maps for surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.QA","authors_text":"Hyun Kyu Kim","submitted_at":"2021-04-13T15:22:33Z","abstract_excerpt":"Fock-Goncharov's moduli spaces $\\mathscr{X}_{{\\rm PGL}_3,\\frak{S}}$ of framed ${\\rm PGL}_3$-local systems on punctured surfaces $\\frak{S}$ provide prominent examples of cluster $\\mathscr{X}$-varieties and higher Teichm\\\"uller spaces. In a previous paper of the author (arXiv:2011.14765), building on the works of others, the so-called ${\\rm SL}_3$ quantum trace map is constructed for each triangulable punctured surface $\\frak{S}$ and an ideal triangulation $\\Delta$ of $\\frak{S}$, as a homomorphism from the stated ${\\rm SL}_3$-skein algebra of the surface to a quantum torus algebra that deforms t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.06286","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/2104.06286/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"}