Complex Hyperbolic Triangle Groups

摘要

The theory of complex hyperbolic discrete groups is still in its childhood hut 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. Those 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.