Complex Kleinian Groups

Author : Angel Cano
Publisher : Springer Science & Business Media
ISBN 13 : 3034804814
Total Pages : 288 pages
Book Rating : 4.13/5 ( download)

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Download or read book Complex Kleinian Groups written by Angel Cano and published by Springer Science & Business Media. This book was released on 2012-11-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.​

Author : Katsuhiko Matsuzaki
Publisher : Clarendon Press
ISBN 13 : 0191591203
Total Pages : 265 pages
Book Rating : 4.04/5 ( download)

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Download or read book Hyperbolic Manifolds and Kleinian Groups written by Katsuhiko Matsuzaki and published by Clarendon Press. This book was released on 1998-04-30 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

Author : Springer
Publisher :
ISBN 13 : 9783034804820
Total Pages : 294 pages
Book Rating : 4.22/5 ( download)

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Download or read book Complex Kleinian Groups written by Springer and published by . This book was released on 2012-11-07 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Samuil Leĭbovich Krushkalʹ
Publisher : American Mathematical Soc.
ISBN 13 : 0821845160
Total Pages : 212 pages
Book Rating : 4.65/5 ( download)

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Download or read book Kleinian Groups and Uniformization in Examples and Problems written by Samuil Leĭbovich Krushkalʹ and published by American Mathematical Soc.. This book was released on 1986 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified exposition of the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. This book lists the basic facts regarding Kleinian groups and serves as a general guide to the primary literature, particularly the Russian literature in the field.

Author : Michael Kapovich
Publisher : Springer Science & Business Media
ISBN 13 : 0817649131
Total Pages : 470 pages
Book Rating : 4.35/5 ( download)

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Download or read book Hyperbolic Manifolds and Discrete Groups written by Michael Kapovich and published by Springer Science & Business Media. This book was released on 2009-08-04 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

Author : Yair N. Minsky
Publisher : Cambridge University Press
ISBN 13 : 1139447211
Total Pages : 399 pages
Book Rating : 4.18/5 ( download)

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Download or read book Spaces of Kleinian Groups written by Yair N. Minsky and published by Cambridge University Press. This book was released on 2006-06-19 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development. This volume contains important expositions on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory and computer explorations. Researchers in these and related areas will find much of interest here.

Author : A. Marden
Publisher : Cambridge University Press
ISBN 13 : 1139463764
Total Pages : 393 pages
Book Rating : 4.68/5 ( download)

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Download or read book Outer Circles written by A. Marden and published by Cambridge University Press. This book was released on 2007-05-31 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

Author : David Mumford
Publisher : Cambridge University Press
ISBN 13 : 9780521352536
Total Pages : 422 pages
Book Rating : 4.33/5 ( download)

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Download or read book Indra's Pearls written by David Mumford and published by Cambridge University Press. This book was released on 2002-04-25 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries. For a century these ideas barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

Author : Samuil Leĭbovich Krushkalʹ
Publisher :
ISBN 13 : 9781470444761
Total Pages : pages
Book Rating : 4.63/5 ( download)

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Download or read book Kleinian Groups and Uniformization in Examples and Problems written by Samuil Leĭbovich Krushkalʹ and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at researchers, graduate students and undergraduates alike, this book presents a unified exposition of all the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. The past 20 years have seen a rejuvenation of the field, due to the development of powerful new methods in topology, the theory of functions of several complex variables, and the theory of quasiconformal mappings. Thus this new book should provide a valuable resource, listing the basic facts regarding Kleinian groups and serving as a general guide to the primary literature, par.

Author : C. S. Aravinda
Publisher : American Mathematical Soc.
ISBN 13 : 0821898825
Total Pages : 369 pages
Book Rating : 4.26/5 ( download)

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Download or read book Geometry, Groups and Dynamics written by C. S. Aravinda and published by American Mathematical Soc.. This book was released on 2015-05-01 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.