{"paper":{"title":"Genealogy of Nonperturbative Quantum-Invariants of 3-Manifolds: The Surgical Family","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Thomas Kerler","submitted_at":"1996-01-21T02:36:20Z","abstract_excerpt":"We study the relations between the invariants $\\tau_{RT}$, $\\tau_{HKR}$, and\n $\\tau_L$ of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko,\n respectively. In particular, we discuss explicitly how $\\tau_L$ specializes to $\\tau_{RT}$ for semisimple categories and to $\\tau_{HKR}$ for Tannakian categories. We give arguments for that $\\tau_L$ is the most general invariant that stems from an extended TQFT. We introduce a canonical, central element, {\\sf Q}, for a quasi-triangular Hopf algebra, $\\A$, that allows us to apply the Hennings algorithm directly, in order to compute $\\tau_{RT}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9601021","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"}