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.

中文翻译：

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FC 型 Artin 群中的抛物线子群

摘要 抛物线子群是 Artin 群的组成部分。本文将 Cumplido、Gebhardt、Gonzales-Meneses 和 Wiest 的先前结果（仅以有限类型 Artin 群的抛物线子群已知）扩展到 FC 类型 Artin 群的抛物线子群。我们证明了有限类型抛物线子群的类在交集下是封闭的。我们还研究了 Cumplido 等人构建的映射类组的曲线复合体的模拟。使用抛物线子群。我们将这个称为抛物线子群的复合体的构造扩展到 FC 型 Artin 群。我们表明，在大多数情况下，这个单纯复形是无限大的，并推测它是 δ-双曲的。