Topology and Group Theory Seminar: January 29, 2025
Speaker: Abdul Zalloum (University of Toronto)
Title: From coarse to fine: a generalized Sageev’s construction in hyperbolic spaces
Abstract: I will discuss a construction that starts with a set S, a collection of bi-partitions on S called walls, and produces a spectrum of metric spaces, including Helly graphs, hyperbolic spaces, and injective metric spaces. The resulting space depends on the combinatorics of the walls; for example, if pairs of points are separated by finitely many walls, the resulting metric space is exactly Sageev’s dual CAT(0) cube complex. I will also discuss a range of applications of this construction, with focus on the most recent: in joint work with Petyt-Spriano, we use the above framework to show that residually finite hyperbolic groups admit globally stable cylinders, addressing a question of Rips-Sela who asked in 1995 whether torsion-free hyperbolic groups possess such cylinders.
Host: Dan Margalit