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OverviewThis 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. Full Product DetailsAuthor: Angel Cano , Juan Pablo Navarrete , José SeadePublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 2013 ed. Volume: 303 Dimensions: Width: 15.50cm , Height: 1.60cm , Length: 23.50cm Weight: 4.453kg ISBN: 9783034808057ISBN 10: 3034808054 Pages: 272 Publication Date: 14 December 2014 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreface.- 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.ReviewsFrom 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) 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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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