Return to Colloquia & Seminar listing

### Relatively geometric actions of complex hyperbolic lattices on CAT(0) cube complexes

**Geometry/Topology**

Speaker: | Kejia Zhu, University of Illinois Chicago |

Location: | Zoom Zoom |

Start time: | Tue, Jan 24 2023, 1:10PM |

We prove that for $n\geq 2$, a non-uniform lattice in $PU(n,1)$ does not admit a relatively geometric action on a CAT(0) cube complex. As a consequence, we prove that if $\Gamma$ is a non-uniform lattice in a non-compact semisimple Lie group $G$ that admits a relatively geometric action on a CAT(0) cube complex, then $G$ is isomorphic to $SO(n,1)$. We also prove that given a relatively hyperbolic group with residually finite parabolic subgroups, if it is Kahler and acts relatively geometrically on a CAT(0) cube complex, then it is virtually a surface group. This work is joint with Corey Bregman and Daniel Groves.