Balanced walls for random groups
Group Theory
2018-12-13 v2
Abstract
We study a random group G in the Gromov density model and its Cayley complex X. For density < 5/24 we define walls in X that give rise to a nontrivial action of G on a CAT(0) cube complex. This extends a result of Ollivier and Wise, whose walls could be used only for density < 1/5. The strategy employed might be potentially extended in future to all densities < 1/4.
Cite
@article{arxiv.1407.0332,
title = {Balanced walls for random groups},
author = {John M. Mackay and Piotr Przytycki},
journal= {arXiv preprint arXiv:1407.0332},
year = {2018}
}
Comments
18 pages, 2 figures. v2: Minor improvements, final version