On Spherical CR Uniformization of 3-Manifolds

Abstract

We consider the discrete representations of 3-manifold groups into that appear in the Falbel–Koseleff–Rouillier census such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. This illustrates the fact that a discrete representation with cyclic unipotent boundary holonomy is not in general the holonomy of a spherical CR uniformization of M.

2000 AMS Subject Classification::

• 32V05
• 57M50
• 22E40

Keywords:

• Hyperbolic geometry
• complex geometry
• discrete groups