Geodesic
A uniformizable spherical CR structure on a two-cusped hyperbolic 3–manifold
Jiang, Yueping1 ; Wang, Jieyan1 ; Xie, Baohua1
1 School of Mathematics, Hunan University, Changsha, China
Algebraic and Geometric Topology, Tome 23 (2023) no. 9, pp. 4143-4184

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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.

DOI : 10.2140/agt.2023.23.4143
Keywords: complex hyperbolic space, spherical CR uniformization, triangle groups, Ford domain, hyperbolic $3$–manifolds

Jiang, Yueping 1 ; Wang, Jieyan 1 ; Xie, Baohua 1

1 School of Mathematics, Hunan University, Changsha, China 
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Jiang, Yueping; Wang, Jieyan; Xie, Baohua. A uniformizable spherical CR structure on a two-cusped hyperbolic 3–manifold. Algebraic and Geometric Topology, Tome 23 (2023) no. 9, pp. 4143-4184. doi: 10.2140/agt.2023.23.4143

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