Speaker: Suraj Krishna
Date: December 26, 2023
Affiliation: Technion, Israel

Abstract: A group is cubulated if it acts properly and cocompactly on a CAT(0) cube complex, which is a generalisation of a product of trees. Some well-known examples are free groups, surface groups and fundamental groups of closed hyperbolic 3-manifolds. <p> I will show in the talk that semidirect products of hyperbolic groups with $\mathbb{Z}$ which are again hyperbolic are cubulated, and give some consequences. Two prominent examples of our setup are </p> <p> (1) mapping tori of fundamental groups of closed hyperbolic surfaces over pseudo-Anosov automorphisms, and </p> <p>(2) mapping tori of free groups over atoroidal automorphisms. </p> Both these classes of groups are known to be cubulated by outstanding works. Our proof uses these two noteworthy results as building blocks and places them in a unified framework. Based on joint work with François Dahmani and Jean Pierre Mutanguha.