Complex hyperbolic triangle groups

Abstract

The theory of complex hyperbolic discrete groups is still in its childhood but promises to grow into a rich subfield of geometry. In this paper I will discuss some recent progress that has been made on complex hyperbolic deformations of the modular group and, more generally, triangle groups. These are some of the simplest nontrivial complex hyperbolic discrete groups. In particular, I will talk about my recent discovery of a closed real hyperbolic 3-manifold which appears as the manifold at infinity for a complex hyperbolic discrete group.

Cited by in corpus (18)

• New non-arithmetic complex hyperbolic lattices
• Locally homogeneous geometric manifolds
• A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
• An explicit fundamental domain for the Picard modular group in two complex dimensions
• On the type of triangle groups
• A uniformizable spherical CR structure on a two-cusped hyperbolic 3-manifold
• The moduli space of points in quaternionic projective space
• Non-Discrete Complex Hyperbolic Triangle Groups of Type (m,m,infinity)
• Kleinian groups in higher dimensions
• Generators of a Picard modular group in two complex dimensions
• Generators for the Euclidean Picard Modular Groups
• Slim curves, limit sets and spherical CR uniformisations
• On the limit set of a spherical CR uniformization
• Rank 1 deformations of non-cocompact hyperbolic lattices
• Arithmeticity of complex hyperbolic triangle groups
• Traces in Complex Hyperbolic Triangle Groups
• Groups generated by two elliptic elements in PU(2,1)
• Classification of complex hyperbolic triangle groups by types