Curve diagrams for Artin groups of type B

DOI10.14492/HOKMJ/1478487616zbMATH Open1378.20051arXiv1310.0546OpenAlexW2548986983MaRDI QIDQ340999

Tetsuya Ito

Publication date: 15 November 2016

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

Abstract: We develop a theory of curve diagrams for Artin groups of type B. We define the winding number labeling and the wall crossing labeling of curve diagrams, and show that these labelings detect the classical and the dual Garside length, respectively. A remarkable point is that our argument does not require Garside theory machinery like normal forms, and is more geometric in nature.

Full work available at URL: https://arxiv.org/abs/1310.0546

zbMATH Keywords

Artin groupcurve diagramGarside structure

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Generators, relations, and presentations of groups (20F05) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

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