Complex Kleinian Groups

• Main Authors: Cano, Angel (Author), Navarrete, Juan Pablo (Author), Seade, José (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
• Series: Progress in Mathematics ; 303
• Subjects: Mathematics.; Topological groups.; Lie groups.; Dynamics.; Ergodic theory.; Functions of complex variables.; Dynamical Systems and Ergodic Theory.; Topological Groups, Lie Groups.; Several Complex Variables and Analytic Spaces.

This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sph...

Table of Contents:

•   Preface
• Introduction
• Acknowledgments
• 1 A glance of the classical theory
• 2 Complex hyperbolic geometry
• 3 Complex Kleinian groups
• 4 Geometry and dynamics of automorphisms of P2C
• 5 Kleinian groups with a control group
• 6 The limit set in dimension two
• 7 On the dynamics of discrete subgroups of PU(n,1)
• 8 Projective orbifolds and dynamics in dimension two
• 9 Complex Schottky groups
• 10 Kleinian groups and twistor theory
• Bibliography
• Index.  .