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On the limit set of a spherical CR uniformization

### Miguel Acosta

Algebraic & Geometric Topology 22 (2022) 3305–3325
##### 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 $ℝ$–circles 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.

##### Keywords
Spherical CR, limit set, triangle group, complex hyperbolic geometry, horotube, $(G,X)$–structures
##### Mathematical Subject Classification 2010
Primary: 22E40, 57M50
Secondary: 37C85, 51M10