On the limit set of a spherical CR uniformization

Abstract

We explore the limit set of a particular spherical CR uniformization of a cusped hyperbolic manifold. We prove that the limit set is the closure of a countable union of $\mathbb{R}$-circles, is connected, and contains a Hopf link with three components; we also show that the fundamental group of its complement in $S^3$ is not finitely generated. Additionally, we prove that rank-one spherical CR cusps are quotients of horotubes.

15 pages, 2 figures, comments are welcome

References in corpus (5)

• Complex hyperbolic triangle groups
• A complex hyperbolic Riley slice
• Character varieties for real forms
• Spherical CR uniformization of Dehn surgeries of the Whitehead link complement
• Spherical CR Dehn Surgery