The braided Thompson's groups are of type F∞

By Kai-Uwe Bux, Martin G. Fluch, Marco Marschler, Stefan Witzel, Matthew C. b. Zaremsky. 2012

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Abstract We prove that the braided Thompson’s groups Vbr{V_{\mathrm{br}}} and Fbr{F_{\mathrm{br}}} are of type F∞{\rm 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/248a6d26c870eb8c33b2fcc5fcb0d324a9d254d7