Complex Kleinian Groups: 303 (Progress in Mathematics, 303)

Cano, Angel

ISBN 10: 3034804806 / ISBN 13: 9783034804806

Published by Birkhäuser, 2012

About this Item

This book explores complex Kleinian groups, a new area of mathematics born in the work of Riemann, Poincare, Picard and others. The author brings together classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and more. Series: Progress in Mathematics. Num Pages: 272 pages, biography. BIC Classification: PBF; PBG; PBKD; PBWR. Category: (P) Professional & Vocational. Dimension: 243 x 161 x 22. Weight in Grams: 582. . 2012. 2013th Edition. hardcover. . . . . Books ship from the US and Ireland.

Seller Inventory # V9783034804806

Bibliographic Details

• Title: Complex Kleinian Groups: 303 (Progress in Mathematics, 303)
• Publisher: Birkhäuser
• Publication Date: 2012
• Language: English
• ISBN 10: 3034804806
• ISBN 13: 9783034804806
• Binding: Hardcover
• Condition: New

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.