The braided Thompson's groups are of type F∞-Reference-Cited by-同舟云学术

The braided Thompson's groups are of type F∞

Published:2014-05-20 Issue:718 Volume:2016 Page:59-101
ISSN:1435-5345
Container-title:Journal für die reine und angewandte Mathematik
language:en
Short-container-title:

Author:

Bux Kai-Uwe¹,Fluch Martin G.¹,Marschler Marco¹,Witzel Stefan²,Zaremsky Matthew C. B.³

Affiliation:

1. Department of Mathematics , Bielefeld University , 33501 Bielefeld , Germany

2. Mathematical Institute , University of Münster , 48149 Münster , Germany

3. Department of Mathematical Sciences , Binghamton University , Binghamton , NY 13902 , USA

Abstract

Abstract We prove that the braided Thompson’s groups V br

{V_{\mathrm{br}}}

and F br

{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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2014-0030/pdf

Reference34 articles.

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