{"paper":{"title":"Garside theory and subsurfaces: some examples in braid groups","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Bert Wiest, Saul Schleimer","submitted_at":"2018-07-04T09:42:46Z","abstract_excerpt":"Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomial in the length of the braids. In this paper we suggest a more precise bound: for rigid braids with $N$ strands and of Garside length $L$, the sliding circuit set should have at most $C\\cdot L^{N-2}$ elements, for some constant $C$. We construct a family of braids which realise t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01500","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":""},"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"}