Homological stability for Artin monoids

TL;DR

This paper proves homological stability for certain sequences of Artin monoids, including braid monoids, and extends known stability results for Artin groups of types A, B, and D, under the $K( pi,1)$ conjecture.

Contribution

It establishes homological stability for sequences of Artin monoids and groups, extending classical results to new types under the $K( pi,1)$ conjecture.

Findings

Homological stability proven for specific Artin monoids.

Stability results extended to Artin groups of types B and D.

Results depend on the $K( pi,1)$ conjecture for associated groups.

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 $D$.