New constructions of fundamental polyhedra in complex hyperbolic space

DOI10.1007/BF02393220zbMath1113.22010MaRDI QIDQ2495344

Martin Deraux, Julien Paupert, Elisha Falbel

Publication date: 6 July 2006

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

complex hyperbolic spacebisectorsDirichlet domainsEisenstein-Picard group

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Discrete subgroups of Lie groups (22E40) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45)

Related Items (15)

Generators for the Euclidean Picard modular groups ⋮ Generators of the sister of Euclidean Picard modular groups ⋮ Similarity classes of tetrahedra ⋮ The geometry of the Gauss-Picard modular group ⋮ Non-arithmetic hybrid lattices in \(\text{PU}(2,1)\) ⋮ Notes on complex hyperbolic triangle groups ⋮ New nonarithmetic complex hyperbolic lattices. II ⋮ Census of the Complex Hyperbolic Sporadic Triangle Groups ⋮ Cone metrics on the sphere and Livné's lattices ⋮ The geometry of the Eisenstein-Picard modular group ⋮ Generators of a Picard modular group in two complex dimensions ⋮ A minimal volume arithmetic cusped complex hyperbolic orbifold ⋮ Fundamental domains and presentations for the Deligne-Mostow lattices with 2-fold symmetry ⋮ Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere ⋮ New non-arithmetic complex hyperbolic lattices

Cites Work

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• On a remarkable class of polyhedra in complex hyperbolic space
• Real hyperbolic on the outside, complex hyperbolic on the inside
• Rigidity and flexibility of triangle groups in complex hyperbolic geometry
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Generalized Picard lattices arising from half-integral conditions
• Fundamental domains for finite subgroups in \(U(2)\) and configurations of Lagrangians
• The geometry of the Eisenstein-Picard modular group
• Dirichlet Domains for the Mostow Lattices

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