Complex hyperbolic triangle groups

Details Complex hyperbolic triangle groups Complex hyperbolic triangle groups

2003-04-18

arxiv.org/abs/math/0304268v1

Proceedings of the ICM, Beijing 2002, vol. 2, 339--350

Mathematics

Differential Geometry

Scientific paper

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.

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