On Belk's classifying space for Thompson's group F
Abstract
The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to braids, except instead of braiding the strands split and merge. In Belk's thesis, a space CF was considered, of configurations of points on the real line allowing for splitting and merging, and a proof was sketched that CF is a classifying space for F. The idea there was to build the universal cover and construct an explicit contraction to a point. Here we start with an established CAT(0) cube complex X on which F acts freely, and construct an explicit homotopy equivalence between X/F and CF, proving that CF is indeed a K(F,1).
Keywords
Cite
@article{arxiv.1306.6534,
title = {On Belk's classifying space for Thompson's group F},
author = {Lucas Sabalka and Matthew C. B. Zaremsky},
journal= {arXiv preprint arXiv:1306.6534},
year = {2014}
}
Comments
v2 is a significant rewrite of v1. An error was found in Lemma 4.5 of v1, invalidating the last 25% of the paper. As such, v2 comprises the first part of v1, with some related necessary revisions. The main result about Thompson's group F remains unchanged. v2 has 12 pages and 4 figures