Complex Kleinian Groups

Angel Cano|Juan Pablo Navarrete|José Seade

ISBN 10: 3034808054 / ISBN 13: 9783034808057

Published by Springer Basel, 2014

About this Item

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Lays down the foundations of a new field of mathematics including areas as important as real and complex hyperbolic geometry, discrete group actions in complex geometry and the uniformization problemFirst book of its kind in the literature .

Seller Inventory # 4318377

Bibliographic Details

• Title: Complex Kleinian Groups
• Publisher: Springer Basel
• Publication Date: 2014
• Language: English
• ISBN 10: 3034808054
• ISBN 13: 9783034808057
• Binding: Soft cover
• Condition: New
• Seller catalogs:
  • Mathematik/Naturwissenschaften/Technik/Medizin

About this title

Synopsis

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces 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 be regarded too as being groups of holomorphic automorphisms of the complex projective line CP¹. When going 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 are different 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 case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​

From the Back Cover

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.