# A new cubulation theorem for hyperbolic groups

 Geometric Structures on 3-manifolds Topic: A new cubulation theorem for hyperbolic groups Speaker: Daniel Groves Affiliation: University of Illinois, Chicago Date: Tuesday, October 27 Time/Room: 4:00pm - 5:00pm/S-101 Video Link: https://video.ias.edu/gsm/2015/1027-Groves2

We prove that if a hyperbolic group $G$ acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then $G$ is virtually special. This generalizes Agol's Theorem (the case when the action is proper) and Wise's Quasiconvex Hierarchy Theorem (the case when the cube complex is a tree). This is joint work in preparation with Jason Manning.