Rigidity and classification results for large-type Artin groups

TL;DR

This paper investigates the automorphism groups and rigidity properties of large-type Artin groups by analyzing their intersection graphs, leading to new classification and rigidity results across various mathematical contexts.

Contribution

It introduces the automorphism group of the intersection graph for large-type Artin groups and derives multiple rigidity and classification results.

Findings

Computed automorphism groups of intersection graphs.

Established rigidity of lattice embeddings and von Neumann algebras.

Classified groups up to quasi-isometry and measure equivalence.

Abstract

We compute the automorphism group of the intersection graph of many large-type Artin groups. This graph is an analogue of the curve graph of mapping class groups but in the context of Artin groups. As an application, we deduce a number of rigidity and classification results for these groups, including computation of outer automorphism groups, commensurability classification, quasi-isometric rigidity, measure equivalence rigidity, orbit equivalence rigidity, rigidity of lattice embedding, and rigidity of cross-product von Neumann algebra.