Hyperbolicity of the complex of parabolic subgroups of Artin-Tits groups of type $B$

TL;DR

This paper proves that the complex of parabolic subgroups in Artin-Tits groups of type B exhibits hyperbolic geometry, contributing to the understanding of their geometric properties.

Contribution

It establishes the hyperbolicity of the complex of parabolic subgroups specifically for Artin-Tits groups of type B, a new result in geometric group theory.

Findings

The complex of parabolic subgroups is hyperbolic.

Provides new insights into the geometric structure of Artin-Tits groups of type B.

Advances understanding of subgroup complexes in algebraic groups.

Abstract

We show that the complex of parabolic subgroups associated to the Artin-Tits group of type $B$ is hyperbolic