Property $R_\infty$ for new classes of Artin groups

TL;DR

This paper proves property R_infinity for specific classes of Artin groups, including spherical type D_n and certain hyperbolic-type groups, using automorphism group descriptions and hyperbolic space actions.

Contribution

It establishes property R_infinity for new classes of Artin groups and provides a detailed proof of Delzant's Lemma, enhancing understanding of automorphisms and hyperbolic actions.

Findings

Property R_infinity holds for Artin groups of spherical type D_n, n≥6.

R_infinity also holds for certain hyperbolic-type free-of-infinity Artin groups.

The paper offers a detailed proof of Delzant's Lemma.

Abstract

We establish property $R_\infty$ for Artin groups of spherical type $D_n$, $n\ge6$, their central quotients, and also for large hyperbolic-type free-of-infinity Artin groups and some other classes of large-type Artin groups. The key ingredients are recent descriptions of the automorphism groups for these Artin groups and their action on suitable Gromov-hyperbolic spaces. We also provide a detailed proof of Delzant's Lemma, an important technical tool used in our work and in several other papers on the $R_\infty$ property.