An explicit fundamental domain for the Picard modular group in two complex dimensions

Gábor Francsics; Peter D. Lax

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An explicit fundamental domain for the Picard modular group in two complex dimensions

Gábor Francsics·Peter D. Lax

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Abstract

Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space ${\bf CH}^{2}$. The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in ${\bf C}^2$ equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of $SU(2,1)$ with Gaussian integer entries. This fundamental domain has finite volume, one cusp, explicitly given boundary surfaces and an interesting symmetry.

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BibTeX RIS

Gábor Francsics, Peter D. Lax. 2005-09-29. An explicit fundamental domain for the Picard modular group in two complex dimensions. https://arxiv.org/abs/math/0509708

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