Spaces Of Kleinian Groups

Author : Yair Nathan Minsky
Publisher :
ISBN 13 : 9781139111935
Total Pages : 390 pages
Book Rating : 4.30/5 ( download)

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Download or read book Spaces of Kleinian Groups written by Yair Nathan Minsky and published by . This book was released on 2006 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important and original research in the fast-developing subject of Kleinian groups and hyperbolic 3-manifolds.

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 : 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 : Walter Lawrence Lok
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.18/5 ( download)

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Download or read book Deformations of Locally Homogeneous Spaces and Kleinian Groups written by Walter Lawrence Lok and published by . This book was released on 1985 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John H. Holt
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.09/5 ( download)

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Download or read book The Global Topology of Deformation Spaces of Kleinian Groups written by John H. Holt and published by . This book was released on 2000 with total page 154 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 : L. Bers
Publisher : Springer
ISBN 13 : 354037776X
Total Pages : 140 pages
Book Rating : 4.64/5 ( download)

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Download or read book A Crash Course on Kleinian Groups written by L. Bers and published by Springer. This book was released on 2006-11-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bernard Maskit
Publisher : Springer Science & Business Media
ISBN 13 : 3642615902
Total Pages : 339 pages
Book Rating : 4.00/5 ( download)

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Download or read book Kleinian Groups written by Bernard Maskit and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations. From the point of view of uniformizations of Riemann surfaces, Bers' observation has the consequence that the question of understanding the different uniformizations of a finite Riemann surface poses a purely topological problem; it is independent of the conformal structure on the surface. The last two chapters here give a topological description of the set of all (geometrically finite) uniformizations of finite Riemann surfaces. We carefully skirt Ahlfors' finiteness theorem. For groups which uniformize a finite Riemann surface; that is, groups with an invariant component, one can either start with the assumption that the group is finitely generated, and then use the finiteness theorem to conclude that the group represents only finitely many finite Riemann surfaces, or, as we do here, one can start with the assumption that, in the invariant component, the group represents a finite Riemann surface, and then, using essentially topological techniques, reach the same conclusion. More recently, Bill Thurston wrought a revolution in the field by showing that one could analyze Kleinian groups using 3-dimensional hyperbolic geome try, and there is now an active school of research using these methods.

Author : Mikhail Kapranov
Publisher : Springer Science & Business Media
ISBN 13 : 9783764386085
Total Pages : 742 pages
Book Rating : 4.88/5 ( download)

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Download or read book Geometry and Dynamics of Groups and Spaces written by Mikhail Kapranov and published by Springer Science & Business Media. This book was released on 2008-03-05 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.