Curve diagram for Artin group of type B

2013/10/02 by Tetsuya Ito, Ito, Tetsuya · 1 citation
Mathematics · Medicine · #20F10 #20F36 #57M07 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1310.0546

openalex publication_date 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups

Cited by

• Curves in the disc, the type B braid group, and the type B zigzag algebra

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