Arithmetic hyperbolic manifolds and their fundamental groups

Speaker:Hongbin Sun (Rutgers University–New Brunswick)

Time: 2026-02-04 09:15-11:15
Zoom Meeting ID: 948 7218 1211 Passcode: 263298

Abstract:

In the first lecture, I will give an introduction to arithmetic hyperbolic manifolds, using the hyperboloid model.

In the second lecture, I will describe a difference between dimensions <4 and higher dimensions: the fundamental group of a 2- or 3-dimensional hyperbolic manifold is LERF, and the fundamental group of an arithmetic hyperbolic manifold of dimension at least 4 is not LERF.
Here LERF is a purely group-theoretic property that is very useful in low-dimensional topology.