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arXiv · 1410.0923

Homological stability for subgroups of surface braid groups

TriThang Tran
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Abstract

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 $ξ$ 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.

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TriThang Tran. 2014-10-03. Homological stability for subgroups of surface braid groups. https://arxiv.org/abs/1410.0923

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