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


Pierre Will
Universite Grenoble-Alpes


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.


Differential Geometry Seminar
Friday, April 9
10:00am MST
Online via Zoom
Email Julien Paupert for the Zoom link