Spaces Of Kleinian Groups
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Spaces Of Kleinian Groups
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Author : Yair Nathan Minsky
language : en
Publisher:
Release Date : 2006
Spaces Of Kleinian Groups written by Yair Nathan Minsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Geometry, Hyperbolic categories.
Important and original research in the fast-developing subject of Kleinian groups and hyperbolic 3-manifolds.
Complex Kleinian Groups
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Author : Angel Cano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-05
Complex Kleinian Groups written by Angel Cano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-05 with Mathematics categories.
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.
Geometry And Dynamics Of Groups And Spaces
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Author : Mikhail Kapranov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-05
Geometry And Dynamics Of Groups And Spaces written by Mikhail Kapranov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-05 with Mathematics categories.
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.
Kleinian Groups
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Author : Bernard Maskit
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Kleinian Groups written by Bernard Maskit and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Hyperbolic Manifolds And Kleinian Groups
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Author : Katsuhiko Matsuzaki
language : en
Publisher: Clarendon Press
Release Date : 1998-04-30
Hyperbolic Manifolds And Kleinian Groups written by Katsuhiko Matsuzaki and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-30 with Mathematics categories.
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.
Conformal Geometry Of Discrete Groups And Manifolds
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Conformal Geometry Of Discrete Groups And Manifolds written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Discrete Groups In Space And Uniformization Problems
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Author : B. Apanasov
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-06-30
Discrete Groups In Space And Uniformization Problems written by B. Apanasov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-30 with Mathematics categories.
A revised and substantially enlarged edition of the Russian book Discrete transformation groups and manifold structures published by Nauka in 1983, this volume presents a comprehensive treatment of the geometric theory of discrete groups and the associated tessellations of the underlying space. Also dealt with in depth are geometric and conformal structures on manifolds, with particular emphasis on hyperbolic n-dimensional manifolds. A detailed account of the geometric and analytic properties of geometrically-finite Mobius groups in n-dimensional space is given and this forms the basis of the subsequent analysis. Emphasis is placed on the geometrical aspects and on the universal constraints which must be satisfied by all tessellations and structures on manifolds. Annotation copyrighted by Book News, Inc., Portland, OR
Hyperbolic Manifolds And Discrete Groups
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Author : Michael Kapovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-04
Hyperbolic Manifolds And Discrete Groups written by Michael Kapovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-04 with Mathematics categories.
The main goal of the book is to present a proof of the following. Thurston's Hyperbolization Theorem ("The Big Monster"). Suppose that M is a compact atoroidal Haken 3-manifold that has zero Euler characteristic. Then the interior of M admits a complete hyperbolic metric of finite volume. This theorem establishes a strong link between the geometry and topology 3 of 3-manifolds and the algebra of discrete subgroups of Isom(JH[ ). It completely changed the landscape of 3-dimensional topology and theory of Kleinian groups. Further, it allowed one to prove things that were beyond the reach of the standard 3-manifold technique as, for example, Smith's conjecture, residual finiteness of the fundamental groups of Haken manifolds, etc. In this book we present a complete proof of the Hyperbolization Theorem in the "generic case." Initially we planned 1 including a detailed proof in the remaining case of manifolds fibered over § as well. However, since Otal's book [Ota96] (which treats the fiber bundle case) became available, only a sketch of the proof in the fibered case will be given here.
Lectures On Quasiconformal Mappings
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Author : Lars Valerian Ahlfors
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-07-14
Lectures On Quasiconformal Mappings written by Lars Valerian Ahlfors and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-14 with Mathematics categories.
Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.
The Mathematical Heritage Of Henri Poincar
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Author : Felix E. Browder
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
The Mathematical Heritage Of Henri Poincar written by Felix E. Browder and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This title presents the written versions this Symposium. It contains two papers by invited speakers who were not able to attend, S S Chern and L Nirenberg.