On the twisted conjugacy problem for 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.

v3: a minor correction in the statement of Corollary 1.2. v2: the result generalised to a larger class of Artin groups, references added. 6 pages, 2 figures, comments are welcome