Representations of 3-manifold groups in PU(2,1), and spherical CR structures.
Friday, April 9, 2021 - 10:00am to 11:00am
Online via Zoom
In this talk I will discuss problems related to the
description of spherical CR structures on 3 manifolds. These are
geometric structures (also known as (X,G)-structures) that are modelled
on the boundary at infinity of the complex hyperbolic plane. These
structures are thus closely related to discrete subgroups of PU(2,1),
which is the isometry group of the complex hyperbolic plane. To describe
such structures, it is useful to understand representations of
fundamental groups of 3-manifolds into PU(2,1). Finding such
representations is often a difficult problem. I will survey known
results on these questions, and try to explain how to "easily" find such
representations. Problems related to configuration spaces and conjugacy
classes in PU(2,1) arise that I will describe.