
Complex Kleinian Groups
Birkhäuser (Publisher)
1st Edition
Published on 6. November 2012
Book
Hardback
XX, 272 pages
978-3-0348-0480-6 (ISBN)
Description
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 CP
1
. 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.
Reviews / Votes
From the reviews:
"The book is written in a clear, accessible manner and selected chapters could easily serve as a text for a graduate course on this topic. It also brings together many results published by the authors, their collaborators and others on this topic, as well as giving open questions and directions for future research." (John R. Parker, Mathematical Reviews, February, 2014)
"A wonderful monograph on complex Kleinian groups which is of great interest for researchers and graduate students in the area of complex Kleinian groups and hyperbolic geometry. Each individual chapter is a unit by itself. . The monograph is very well written and structured. . I strongly recommend it." (Gerhard Rosenberger, zbMATH, Vol. 1267, 2013)More details
Series
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XX, 272 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 21 mm
Weight
606 gr
ISBN-13
978-3-0348-0480-6 (9783034804806)
DOI
10.1007/978-3-0348-0481-3
Schweitzer Classification
Other editions
Additional editions

Angel Cano | Juan Pablo Navarrete | Seade Kuri José Antonio
Complex Kleinian Groups
Book
12/2014
Birkhäuser Verlag GmbH
€53.49
Shipment within 10-15 days

Angel Cano | Juan Pablo Navarrete | José Seade
Complex Kleinian Groups
E-Book
11/2012
1st Edition
Birkhäuser
€53.49
Available for download
Content
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.