# On Belk's classifying space for Thompson's group F

@article{Sabalka2013OnBC,
title={On Belk's classifying space for Thompson's group F},
author={Lucas Sabalka and Matthew C. B. Zaremsky},
journal={arXiv: Group Theory},
year={2013}
}
• Published 27 June 2013
• Mathematics
• arXiv: Group Theory
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…

## References

SHOWING 1-9 OF 9 REFERENCES

We introduce forest diagrams and strand diagrams for elements of Thompson's group F. A forest diagram is a pair of infinite, bounded binary forests together with an order-preserving bijection of the
We construct a braided version BV of Thompson’s group V that surjects onto V . The group V is the third of three well known groups F , T and V created by Thompson in the 1960s that have been heavily
• Mathematics
• 2014
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
Let G be the family of finitely presented infinite simple groups introduced by Higman, generalizing R.J. Thompson’s group of dyadic homeomorphisms of the Cantor set. For each G ∈ G and each integer n
In this paper we study a class of groups which may be described as groups of piecewise linear bijections of a circle or of compact intervals of the real line. We use the action of these groups on
• Mathematics
• 2007
We give a unified solution to the conjugacy problem for Thompson’s groups $$F, \,T$$F,T, and $$V$$V. The solution uses “strand diagrams”, which are similar in spirit to braids and generalize