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A uniformizable spherical CR structure on a two-cusped hyperbolic $3$–manifold

Yueping Jiang, Jieyan Wang and Baohua Xie

Algebraic & Geometric Topology 23 (2023) 4143–4184
Abstract

Let I1,I2,I3 be the complex hyperbolic (4,4,) triangle group. We prove Schwartz’s conjecture that I1,I2,I3 is discrete and faithful if and only if I1I3I2I3 is nonelliptic. If I1I3I2I3 is parabolic, we show that the even subgroup I2I3,I2I1 is the holonomy representation of a uniformizable spherical CR structure on the two-cusped hyperbolic 3–manifold s782 in SnapPy notation.

Keywords
complex hyperbolic space, spherical CR uniformization, triangle groups, Ford domain, hyperbolic $3$–manifolds
Mathematical Subject Classification
Primary: 20H10, 22E40, 51M10, 57M50
References
Publication
Received: 19 April 2021
Revised: 27 February 2022
Accepted: 23 June 2022
Published: 23 November 2023
Authors
Yueping Jiang
School of Mathematics
Hunan University
Changsha
China
Jieyan Wang
School of Mathematics
Hunan University
Changsha
China
Baohua Xie
School of Mathematics
Hunan University
Changsha
China

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