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Geometry & Topology Seminar

Title: Cubulating hyperbolic mapping tori
Speaker: Suraj Krishna (Technion, Israel)
Date: 06 December 2023
Time: 04:00 pm
Venue: LH-3

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 Fran├žois Dahmani and Jean Pierre Mutanguha.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 15 Jul 2024