On the limit set of a spherical CR uniformization

Acosta, Miguel

doi:10.2140/agt.2022.22.3305

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On the limit set of a spherical CR uniformization

Miguel Acosta

Algebraic & Geometric Topology 22 (2022) 3305–3325

DOI: 10.2140/agt.2022.22.3305

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

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/

Volume 22, issue 7 (2022)