A cubulation with no factor system
arXiv:2208.10421 · doi:10.2140/agt.2025.25.255
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.
10 pages, 5 figures; v2: Remarks 2.4 and 3.3 added, to appear in Algebraic & Geometric Topology