Parabolic subgroups in FC-type Artin groups |
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| Authors: | Rose Morris-Wright |
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| Affiliation: | 1. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell''Insubria, Via Valleggio 11, 22100 Como, Italy;2. Dipartimento di Matematica Federigo Enriques, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy;3. Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy;1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain;2. Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium;3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland |
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| Abstract: | Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, 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 by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called 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 δ-hyperbolic. |
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| Keywords: | Artin group Curve complex Parabolic subgroup Extension graph |
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