The braided Thompson's groups are of type F<sub>∞</sub>

Kai‐Uwe Bux, Martin Fluch, Marco Marschler, Stefan Witzel, Matthew C. B. Zaremsky

Type: Article

Publication Date: 2014-05-20

Citations: 43

DOI: https://doi.org/10.1515/crelle-2014-0030

Abstract

Abstract We prove that the braided Thompson’s groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>V</m:mi> <m:mi>br</m:mi> </m:msub> </m:math> {V_{\mathrm{br}}} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>F</m:mi> <m:mi>br</m:mi> </m:msub> </m:math> {F_{\mathrm{br}}} are of type <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="normal">F</m:mi> <m:mi mathvariant="normal">∞</m:mi> </m:msub> </m:math> {\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.

Locations

arXiv (Cornell University) - View - PDF
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Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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+	Conjugacy in Thompson's Groups	2007	James Belk Francesco Matucci
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+	Braids, Links, and Mapping Class Groups	1974	Joan S. Birman
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