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math.GR2022★ 2 cited
A cubulation with no factor system
Sam Shepherd
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 c…
math.GR2022
Semistability of cubulated groups
Sam Shepherd
We prove that all cubulated groups are semistable at infinity. In doing so we prove two further results about cubulations of groups. The first of these states that any one-ended cu…
math.GR2022
Commensurability of lattices in right-angled buildings
Sam Shepherd
Let be a graph product of finite groups, with finite underlying graph, and let be the associated right-angled building. We prove that a uniform lattice in the cubical a…