Produktbild: Complex Kleinian Groups

Complex Kleinian Groups

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Progress in Mathematics 303

ISBN: 3034808054
ISBN 13: 9783034808057
Autor: Cano, Angel/Navarrete, Juan Pablo/Seade, José
Verlag: Springer Basel AG
Umfang: xx, 272 S.
Erscheinungsdatum: 14.12.2014
Auflage: 1/2014
Produktform: Kartoniert
Einband: Kartoniert

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.

Artikelnummer: 7609623 Kategorie:

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