Generators for the Euclidean Picard modular groups

DOI10.1090/S0002-9947-2011-05524-8zbMath1250.22014arXiv1006.3331OpenAlexW2963026025MaRDI QIDQ2884402

Tie-Hong Zhao

Publication date: 29 May 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.3331

zbMATH Keywords

Bianchi groupscomplex hyperbolic spacePicard modular groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Discrete subgroups of Lie groups (22E40) Other groups related to topology or analysis (20F38) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45)

Related Items (8)

Generators of the sister of Euclidean Picard modular groups ⋮ A presentation for the Eisenstein-Picard modular group in three complex dimensions ⋮ On the geometry of a Picard modular group ⋮ Presentations for cusped arithmetic hyperbolic lattices ⋮ Branched sperical CR structures on the complement of the figure-eight knot ⋮ Presentations for the Euclidean Picard modular groups ⋮ A set of generators for the Picard modular group \({SU}(2,1,\mathcal{O}_2)\) ⋮ GENERATORS OF THE EISENSTEIN–PICARD MODULAR GROUP IN THREE COMPLEX DIMENSIONS

Cites Work

• The geometry of the Gauss-Picard modular group
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• New constructions of fundamental polyhedra in complex hyperbolic space
• Cone metrics on the sphere and Livné's lattices
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• Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups
• Generators and relations for certain special linear groups
• Almost-Bieberbach groups: affine and polynomial structures
• A minimal volume arithmetic cusped complex hyperbolic orbifold
• Symmetry Points and Chern Invariants of Picard Modular Surfaces
• Zur groben Klassifikation der Picardschen Modulflächen
• Über die Anzahl der Spitzen einiger arithmetischer Untergruppen unitärer Gruppen
• The Geometries of 3-Manifolds
• Generators of a Picard modular group in two complex dimensions
• A presentation of SL ₂ for Euclidean imaginary quadratic number fields
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