Cubulating hyperbolic mapping tori

par Suraj Krishna (Technion)

jeudi 19 sept. 2024, 14:00 → 15:00 Europe/Paris

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. 

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
(1) mapping tori of fundamental  groups of closed 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 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.