Year: 2022
Type: preprint
Abstract: In this paper we solve the isomorphism problem for all large-type Artin groups. Our strategy involves reconstructing the Coxeter groups associated with large-type Artin groups in a purely algebraic way. This answers several questions raised by Charney. We also study 2-dimensional Artin groups in general. By classifying all their dihedral Artin subgroups, we are able to give strong results of rigidity for all 2-dimensional Artin groups. We prove that "most" standard generators in 2-dimensional Artin groups are preserved under isomorphisms (up to conjugation). We also show that an isomorphism between large-type Artin groups preserves the set of spherical parabolic subgroups if and only if the defining graphs do not have even-labelled leaves. Finally, we show that Artin groups whose defining graphs have even-labelled leaves are never co-Hopfian.
Source: arXiv (Cornell University)
Author: Vaskou, Nicolas
Institution: University of Bristol
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4221160985