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.

Our setup consists of mapping tori of hyperbolic groups which are again hyperbolic. Two prominent examples are (1) mapping tori of fundamental groups of hyperbolic surfaces over pseudo-Anosov automorphisms, and (2) mapping tori of free groups over atoroidal automorphisms. Both these classes of groups are known to be cubulated.

Building on these two important results, and placing them in a unified framework, I will show that all such groups of our setup are cubulated, and explain a few consequences of the result.

This is joint work with François Dahmani and Jean Pierre Mutanguha.

About the Speaker:

He is currently a postdoc at the Technion in Israel, after completing his PhD at the Université Paris Saclay and He was a postdoctoral stint at TIFR. His research area is geometric group theory, specifically CAT(0) cube complexes, hyperbolicity and relative hyperbolicity. Of late, He is learning the interactive theorem prover Lean after developing an interest in the formalisation of mathematics.