{"paper":{"title":"The Tambara-Yamagami categories and 3-manifold invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.GT"],"primary_cat":"math.QA","authors_text":"Leonid Vainerman, Vladimir Turaev","submitted_at":"2010-09-09T14:47:35Z","abstract_excerpt":"We prove that if two Tambara-Yamagami categories TY(A,\\chi,\\nu) and TY(A',\\chi',\\nu') give rise to the same state sum invariants of 3-manifolds and the order of one of the groups A, A' is odd, then \\nu=\\nu' and there is a group isomorphism A\\approx A' carrying \\chi to \\chi'. The proof is based on an explicit computation of the state sum invariants for the lens spaces of type (k,1)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1798","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":""},"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"}