Parabolic subgroups of Artin groups of FC type

DOI10.1016/J.JPAA.2020.106468arXiv1906.07058MaRDI QIDQ6320628

Rose Morris-Wright

Publication date: 17 June 2019

Abstract: Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed using parabolic subgroups. We extend the construction of the complex of parabolic subgroups to FC type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is $delta-$hyperbolic.

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Geometric group theory (20F65) Braid groups; Artin groups (20F36) FC-groups and their generalizations (20F24)

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