Non-positively curved aspects of Artin groups of finite type

Abstract

Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we construct a space (simplicial complex) analogous to Teichmüller space that satisfies a weak nonpositive curvature condition and also a space “at infinity” analogous to the space of projective measured laminations. Using these constructs, we deduce several group-theoretic properties of Artin groups of finite type that are well-known in the case of braid groups.