The braided Thompson's groups are of type F_∞

We prove that the braided Thompson's groups Vbr and Fbr are of type F_\infty, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an appendix, Zaremsky uses these connectivity results to exhibit families of subgroups of the pure braid group that are highly generating, in the sense of Abels and Holz.