Acylindrical hyperbolicity and the centers of Artin groups that are not free of infinity

Fuente: arXiv
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Main Authors: Kato, Motoko, Oguni, Shin-ichi
Format: Preprint
Published: 2024
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_version_ 1866913910581362688
author Kato, Motoko
Oguni, Shin-ichi
author_facet Kato, Motoko
Oguni, Shin-ichi
contents Charney and Morris-Wright showed acylindrical hyperbolicity of Artin groups of infinite type associated with graphs that are not joins, by studying clique-cube complexes and the actions on them. The authors developed their study and clarified when acylindrical hyperbolicity holds for Artin groups of infinite type associated with graphs that are not cones. In this paper, we introduce reduced clique-cube complexes. By using them, we show acylindrical hyperbolicity of irreducible Artin groups associated with graphs that are not cliques, that is, irreducible Artin groups that are not free of infinity. Such Artin groups contain infinite type Artin groups of type FC. As an application, we see that the centers of such Artin groups are finite, and that actually they are trivial in many cases.
format Preprint
id arxiv_https___arxiv_org_abs_2406_09432
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Acylindrical hyperbolicity and the centers of Artin groups that are not free of infinity
Kato, Motoko
Oguni, Shin-ichi
Group Theory
Geometric Topology
20F36, 20F65, 20F67
Charney and Morris-Wright showed acylindrical hyperbolicity of Artin groups of infinite type associated with graphs that are not joins, by studying clique-cube complexes and the actions on them. The authors developed their study and clarified when acylindrical hyperbolicity holds for Artin groups of infinite type associated with graphs that are not cones. In this paper, we introduce reduced clique-cube complexes. By using them, we show acylindrical hyperbolicity of irreducible Artin groups associated with graphs that are not cliques, that is, irreducible Artin groups that are not free of infinity. Such Artin groups contain infinite type Artin groups of type FC. As an application, we see that the centers of such Artin groups are finite, and that actually they are trivial in many cases.
title Acylindrical hyperbolicity and the centers of Artin groups that are not free of infinity
topic Group Theory
Geometric Topology
20F36, 20F65, 20F67
url https://arxiv.org/abs/2406.09432