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Complex Kleinian Groups

  • Angel Cano
  • Juan Pablo Navarrete
  • José Seade

Part of the Progress in Mathematics book series (PM, volume 303)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 1-40
  3. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 41-76
  4. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 77-92
  5. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 93-118
  6. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 119-136
  7. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 137-143
  8. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 145-166
  9. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 167-194
  10. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 195-229
  11. Angel Cano, Juan Pablo Navarrete, José Seade
    Pages 231-251
  12. Back Matter
    Pages 253-271

About this book

Introduction

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 sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds.

Keywords

Kleinian groups complex hyperbolic geometry discontinuity region equicontinuity limit set

Authors and affiliations

  • Angel Cano
    • 1
  • Juan Pablo Navarrete
    • 2
  • José Seade
    • 3
  1. 1., Instituto de MatemáticasUNAM, Unidad CuernavacaCuernavacaMexico
  2. 2., Facultad de MatemáticasUniversidad Autónoma de YucatánMéridaMexico
  3. 3., Facultad de MatemáticasUNAM, Unidad CuernavacaCuernavacaMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0481-3
  • Copyright Information Springer Basel 2013
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0480-6
  • Online ISBN 978-3-0348-0481-3
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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