Homological stability for subgroups of surface braid groups

TriThang Tran

Published 2014-10-03Version 1

In this paper we prove homological stability for certain subgroups of surface braid groups. Alternatively, this is equivalent to proving homological stability for configurations of subsets of exactly $\xi$ points in a surface as we increase the number of subsets. For open surfaces, we prove the result integrally using a variation of the arc complex which we dub the "fern complex". We use a technique of Randal-Williams to extend the result rationally for closed surfaces.