A cubulation with no factor system
Group Theory
2025-03-12 v2
Abstract
The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a construction is not always possible, namely we construct a cubulated group for which the cube complex does not have a factor system. We also construct a cubulated group for which the induced action on the contact graph is not acylindrical.
Keywords
Cite
@article{arxiv.2208.10421,
title = {A cubulation with no factor system},
author = {Sam Shepherd},
journal= {arXiv preprint arXiv:2208.10421},
year = {2025}
}
Comments
10 pages, 5 figures; v2: Remarks 2.4 and 3.3 added, to appear in Algebraic & Geometric Topology