Kleinian groups in higher dimensions

2007/01/13 by Michael Kapovich, Kapovich, Michael · 2 citations
Mathematics · #20F67 #30F40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0701370

openalex publication_date 2007/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space for n greater than 3. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of the hyperbolic 3-space.

Citations

• The Ending Laminations Theorem direct from Teichmuller geodesics

Cited by

• Classification of Quaternionic Projective Transformations by Equicontinuity Regions
• On K3 surfaces with hyperbolic automorphism groups

Related

• The Geometry and Arithmetic of Kleinian Groups
• Geometry and Dynamics of Discrete Isometry Groups of Higher Rank Symmetric Spaces
• Kleinian viewpoints on higher rank worlds
• Lectures on complex hyperbolic Kleinian groups
• Kleinian groups via strict hyperbolization