Homological stability for Artin monoids

Abstract

We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the $K(\pi ,1)$ conjecture holds for the associated family of Artin groups this establishes homological stability for these groups. In particular, this recovers and extends Arnol'd's proof of stability for the Artin groups of type $A$, $B$ and $D$.

50 pages, 4 figures. Final version, to appear in Proceedings of the London Mathematical Society