Discrete Moebius Groups: Fundamental Polyhedra and Convergence

DOI10.2307/2373869zbMath0373.57024OpenAlexW2332302853MaRDI QIDQ4150869

Norbert J. Wielenberg

Publication date: 1977

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2373869

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Groups acting on specific manifolds (57S25) Discrete subgroups of Lie groups (22E40) Differential geometry of symmetric spaces (53C35) Discontinuous groups of transformations (57S30)

Related Items (21)

Compactification via the real spectrum of spaces of classes of representations in \(SO(n,1)\) ⋮ On the representation theory of Möbius groups inR n* ⋮ Discreteness criteria for Möbius groups acting on \(\overline{\mathbb R}^n\) ⋮ DISCRETENESS CRITERIA FOR MÖBIUS GROUPS ACTING ON II ⋮ Topologie de Gromov équivariante, structures hyperboliques et arbres réels. (Equivariant Gromov topology, hyperbolic structures, and \({\mathbb{R}}\)-trees) ⋮ On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality ⋮ Algebraic convergence theorems of \(n\)-dimensional Kleinian groups. ⋮ The exponent of convergence of Poincaré series of combination groups ⋮ Shimizu's lemma for quaternionic hyperbolic space ⋮ Discreteness of subgroups of \(\text{PU}(2,1)\) with regular elliptic elements. ⋮ Discreteness criteria of Möbius groups of high dimensions and convergence theorems of Kleinian groups ⋮ Finiteness and quasi-simplicity for symmetric \(K3\)-surfaces ⋮ Quasiconformal homogeneity of hyperbolic manifolds ⋮ Automorphic quasimeromorphic mappings in \(R^n\) ⋮ Classification of the real discrete specialisations of the Burau representation of B₃ ⋮ The structure of certain subgroups of the Picard group ⋮ Geometrically finite groups of transformations of space ⋮ Differentiability and rigidity of Möbius groups ⋮ On isomorphisms of geometrically finite Möbius groups ⋮ Parabolic vertices and finiteness properties for Kleinian groups in space ⋮ Poincaré series for discrete Moebius groups acting on the upper half space

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