On the twisted conjugacy problem for large-type Artin groups

TL;DR

This paper proves that the twisted conjugacy problem is solvable for certain large-type Artin groups with finite outer automorphism groups, expanding understanding of automorphism structures in these groups.

Contribution

It establishes solvability of the twisted conjugacy problem for a broad class of large-type Artin groups with specific automorphism properties, including new classes like XXXL groups.

Findings

Twisted conjugacy problem is solvable for large-type Artin groups with finite outer automorphism groups.

Includes classes like XXXL Artin groups with specific graph properties.

Provides structural insights into automorphisms of large-type Artin groups.

Abstract

We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversion. This includes XXXL Artin groups whose defining graph is connected, twistless, and not an even edge; and large-type Artin groups whose defining graph admits a twistless hierarchy terminating in twistless stars.