Rigidity and automorphisms of large-type Artin groups

Nicolas Vaskou

Published 2022-01-20Version 1

In this paper we study the automorphisms of large-type Artin groups. In particular, we solve the isomorphism problem for large-type free-of-infinity Artin groups, and we compute completely the automorphism group and the outer automorphism group of these Artin groups. We also give strong rigidity results about the isomorphisms of all large-type Artin groups. Our strategy is geometric and involves reconstructing the Deligne complex in a purely algebraic manner. In particular, we show that the Deligne complexes associated with isomorphic large-type free-of-infinity Artin groups are combinatorially isomorphic. Finally, we give a complete and explicit description of all the dihedral Artin subgroups of large-type Artin groups.