On the limit set of a spherical CR uniformization

DOI10.2140/AGT.2022.22.3305arXiv1910.11042MaRDI QIDQ6327813

Miguel Acosta

Publication date: 24 October 2019

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 $mathbbR$-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.

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Discrete subgroups of Lie groups (22E40) General geometric structures on low-dimensional manifolds (57M50) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85)

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