{"paper":{"title":"Towards an Algebraic Characterization of 3-dimensional Cobordisms","license":"","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.GT","authors_text":"Thomas Kerler","submitted_at":"2001-06-28T21:39:06Z","abstract_excerpt":"The goal of this paper is to find a close to isomorphic presentation of 3-manifolds in terms of Hopf algebraic expressions. To this end we define and compare three different braided tensor categories that arise naturally in the study of Hopf algebras and 3-dimensional topology. The first is the category \\Cob of connected surfaces with one boundary component and 3-dimensional relative cobordisms, the second is a category \\Tgl of tangles with relations, and the third is a natural algebraic category \\Alg freely generated by a Hopf algebra object. From previous work we know that {\\Tgl} and \\Cob ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106253","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":""},"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"}