Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds

Jiming Ma; Baohua Xie

paper

Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds

arXiv:2608.11571

Abstract

Let $s 782$ be the 2-cusped hyperbolic 3-manifold in the SnapPy census. Its spherical CR uniformization was established in \cite{JWX2023} using the Ford domain of the complex hyperbolic triangle group $Δ_{4, 4, \infty; \infty}$ . By comparing the combinatorial structures of the Ford domain of $Δ_{4, 4, \infty; \infty}$ and the Dirichlet domain of $Δ_{4, 4, n; \infty}$ , we prove that for each $n \geq 5$ , the Dehn filling of $s 782$ along the slope $(n - 1) m_{1} + l_{1}$ on its second cusp admits a spherical CR uniformization, where $(m_{1}, l_{1})$ denotes the meridian-longitude system of a cusp in SnapPy notation.

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