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

Abstract

Let $⟨I_1,I_2,I_3⟩$ be the complex hyperbolic $(4,4,\infty )$ triangle group. In this paper we give a proof of a conjecture of Schwartz for $⟨I_1,I_2,I_3⟩$. That is $⟨I_1,I_2,I_3⟩$ is discrete and faithful if and only if $I_1{I}_3{I}_2{I}_3$ is nonelliptic. When $I_1{I}_3{I}_2{I}_3$ is parabolic, we show that the even subgroup $⟨I_2{I}_3,I_2{I}_1⟩$ is the holonomy representation of a uniformizable spherical CR structure on the two-cusped hyperbolic 3-manifold $s782$ in SnapPy notation.

References in corpus (7)

• Complex hyperbolic triangle groups
• A complex hyperbolic Riley slice
• Spherical CR uniformization of Dehn surgeries of the Whitehead link complement
• On spherical CR uniformization of 3-manifolds
• Spherical CR Dehn Surgery
• Branched Spherical CR structures on the complement of the figure eight knot
• Three-manifolds at infinity of complex hyperbolic orbifolds

Cited by in corpus (1)

• Slim curves, limit sets and spherical CR uniformisations