{"paper":{"title":"Kauffman bracket skein modules of small 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.GT","authors_text":"Adam S. Sikora, Efstratia Kalfagianni, Renaud Detcherry","submitted_at":"2023-05-25T15:48:42Z","abstract_excerpt":"The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed $3$-manifolds are finitely generated over $\\mathbb Q(A)$. In this paper, we develop a novel method for computing these skein modules.\n  We show that if the skein module $S(M,\\mathbb Q[A^{\\pm 1}])$ of $M$ is tame (e.g. finitely generated over $\\mathbb Q[A^{\\pm 1}]$), and the $SL(2,\\mathbb\n  C)$-character variety is reduced, then the dimension $\\dim_{\\mathbb Q(A)}\\, S(M, \\mathbb Q(A))$ is the number of closed points in this character variety. This, in particular, verifies a conjecture in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16188","kind":"arxiv","version":3},"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/2305.16188/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"}