On the limit set of a spherical CR uniformization

Miguel Acosta

doi:10.2140/agt.2022.22.3305

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arXiv · 1910.11042

On the limit set of a spherical CR uniformization

Miguel Acosta

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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.

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Miguel Acosta. 2019-10-24. On the limit set of a spherical CR uniformization. https://doi.org/10.2140/agt.2022.22.3305

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