A parabolic action on a proper, CAT(0) cube complex
Abstract
We consider diagram groups as defined by V. Guba and M. Sapir. A diagram group G acts on the associated cube complex K by isometries. It is known that if a cube complex L is of a finite dimension then every isometry g of L is semi-simple, i.e. its translation length is realized. It was conjectured by D. S. Farley that in the case of a diagram group G the action of G on the associated cube complex K is by semisimple isometries even when K has an infinite dimension. In this paper we give a counterexample to Farley Conjecture and we show that R. Thompson's group F, considered as a diagram group, has some elements which act as parabolic (not semi-simple) isometries on the associated cube complex.
Cite
@article{arxiv.1209.5804,
title = {A parabolic action on a proper, CAT(0) cube complex},
author = {Yael Algom-Kfir and Bronislaw Wajnryb and Pawel Witowicz},
journal= {arXiv preprint arXiv:1209.5804},
year = {2012}
}
Comments
This paper was submitted in December 2010 and will appear in Journal of Group Theory