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

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dc.creatorFrancsics, Gábor
dc.creatorLax, Peter D.
dc.date2005-09-29
dc.date.accessioned2026-07-07T06:19:55Z
dc.date.available2026-07-07T06:19:55Z
dc.descriptionOur 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.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0509708
dc.identifierhttp://arxiv.org/abs/math/0509708
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95190
dc.subjectComplex Variables
dc.subjectMetric Geometry
dc.subject22E40; 321M05
dc.titleAn explicit fundamental domain for the Picard modular group in two complex dimensions
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