CAT(0) geometry for the Thompson Group
Group Theory
2012-03-27 v1 Metric Geometry
Abstract
We investigate Farley's CAT(0) cubical model for Thompson's group F (we adopt the classical language of F, using binary trees and piecewise linear maps). Main results include: in general, Thompson's group elements are parabolic; we find simple, exact formulas for the CAT(0) translation lengths, in particular the elements of F are ballistic and uniformly bounded away from zero; there exist flats of any dimension and we construct explicitly many of them; we reveal large regions in the Tits Boundary, for example the positive part of a non-separable Hilbert sphere, but also more complicated objects. En route, we solve several open problems proposed in Farley's papers.
Cite
@article{arxiv.1203.5749,
title = {CAT(0) geometry for the Thompson Group},
author = {Dan-Titus Salajan},
journal= {arXiv preprint arXiv:1203.5749},
year = {2012}
}
Comments
PhD Thesis at EPFL (submitted as such in November 2011)