Many sequences of groups satisfy a phenomenon known as homological stability. In my talk, I will report on recent work proving a homological stability result for sequences of Artin monoids, which are monoids related to Artin and Coxeter groups. From this, one can conclude homological stability for the corresponding sequences of Artin groups, assuming a well-known conjecture in geometric group theory called the K(π,1)-conjecture. This extends the known cases of homological stability for the braid groups and other classical examples.
Joint work with Luigi Caputi generalises these results to a homology stability result for a larger class of monoids - of which Garside and complex braid groups provide interesting examples.