Topology and Related Topics Seminar
Tuesday, 20 February 2024, 12:00-1:00
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Venue: Ramanujan Hall (Hybrid Lecture) (Speaker will be online).
Host: Rekha Santhanam
Speaker: Suraj Krishna
Affiliation: Technion - Israel Institute of Technology
Title: Cubulating hyperbolic mapping tori.
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. Cubulated groups possess remarkable algebraic and geometric features and are an important topic of study in geometric group theory. In this talk, I will show that semidirect products of hyperbolic groups with $\mathbb{Z}$, which are themselves hyperbolic, are cubulated.
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 of these classes of groups are known to be cubulated due to outstanding works. Our proof builds upon these two noteworthy results and places them in a unified framework. This is based on joint work with François Dahmani and Jean Pierre Mutanguha.