Deforming cubulations of hyperbolic groups
Deforming cubulations of hyperbolic groups
We describe a procedure to deform cubulations of hyperbolic groups by 'bending hyperplanes'. Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in fibred hyperbolic 3-manifolds and free-by- Z groups, and Hsu–Wise turns. As an application, we show that every cocompactly cubulated Gromov-hyperbolic group admits a …