Disks in trivial braid diagrams.

DOI10.1016/J.TOP.2003.11.005zbMATH Open1065.20047arXivmath/0311326OpenAlexW2023135880MaRDI QIDQ1879799

Publication date: 23 September 2004

Published in: Topology (Search for Journal in Brave)

Abstract: We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin--Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.

Full work available at URL: https://arxiv.org/abs/math/0311326

zbMATH Keywords

Cayley graphs disks isotopies Garside monoids Artin-Tits groups braid diagrams

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Braid groups; Artin groups (20F36)

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