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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 –circles and contains a Hopf link with three components. We also show that the fundamental group of its complement in S3 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
References
Publication
Received: 13 December 2019
Revised: 20 April 2021
Accepted: 22 September 2021
Published: 30 January 2023
Authors
Miguel Acosta
Unité de recherche en Mathématiques
Université du Luxembourg
Campus Belval
Esch-sur-Alzette
Luxembourg
http://www.normalesup.org/~acosta/