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Author : D.M. Gallo
Publisher : Springer
ISBN 13 : 3540394265
Total Pages : 126 pages
Book Rating : 4.5/5 (43 download)
Download or read book Kleinian Groups and Related Topics written by D.M. Gallo and published by Springer. This book was released on 2006-11-15 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. M. Gallo
Publisher :
ISBN 13 : 9783662206751
Total Pages : 132 pages
Book Rating : 4.2/5 (67 download)
Download or read book Kleinian Groups and Related Topics written by D. M. Gallo and published by . This book was released on 2014-01-15 with total page 132 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 : 4.8/5 (218 download)
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 :
Publisher :
ISBN 13 :
Total Pages : 117 pages
Book Rating : 4.:/5 (859 download)
Download or read book Kleinian Groups and Related Topics written by and published by . This book was released on 1983 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Angel Cano
Publisher : Springer Science & Business Media
ISBN 13 : 3034804814
Total Pages : 288 pages
Book Rating : 4.0/5 (348 download)
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 : Samuil Le_bovich Krushkal_
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898123
Total Pages : 214 pages
Book Rating : 4.8/5 (981 download)
Download or read book Kleinian Groups and Uniformization in Examples and Problems written by Samuil Le_bovich Krushkal_ and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 214 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, particularly the Russian literature in the field. In addition, the book includes a large number of examples, problems, and unsolved problems, many of them presented for the first time.
Author : Samuil Leĭbovich Krushkalʹ
Publisher :
ISBN 13 : 9781470444761
Total Pages : pages
Book Rating : 4.4/5 (447 download)
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 : Y. Komori
Publisher : Cambridge University Press
ISBN 13 : 9781139437233
Total Pages : 396 pages
Book Rating : 4.4/5 (372 download)
Download or read book Kleinian Groups and Hyperbolic 3-Manifolds written by Y. Komori and published by Cambridge University Press. This book was released on 2003-11-10 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jørgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research.
Author : Bernard Maskit
Publisher : Springer Science & Business Media
ISBN 13 : 3642615902
Total Pages : 339 pages
Book Rating : 4.6/5 (426 download)
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 : Yair N. Minsky
Publisher : Cambridge University Press
ISBN 13 : 1139447211
Total Pages : 399 pages
Book Rating : 4.1/5 (394 download)
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 : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821838385
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Author : Kenʼichi Ōshika
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820803
Total Pages : 212 pages
Book Rating : 4.8/5 (28 download)
Download or read book Discrete Groups written by Kenʼichi Ōshika and published by American Mathematical Soc.. This book was released on 2002 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with geometric and topological aspects of discrete groups. The main topics are hyperbolic groups due to Gromov, automatic group theory, invented and developed by Epstein, whose subjects are groups that can be manipulated by computers, and Kleinian group theory, which enjoys the longest tradition and the richest contents within the theory of discrete subgroups of Lie groups. What is common among these three classes of groups is that when seen as geometric objects, they have the properties of a negatively curved space rather than a positively curved space. As Kleinian groups are groups acting on a hyperbolic space of constant negative curvature, the technique employed to study them is that of hyperbolic manifolds, typical examples of negatively curved manifolds. Although hyperbolic groups in the sense of Gromov are much more general objects than Kleinian groups, one can apply for them arguments and techniques that are quite similar to those used for Kleinian groups. Automatic groups are further general objects, including groups having properties of spaces of curvature 0. Still, relationships between automatic groups and hyperbolic groups are examined here using ideas inspired by the study of hyperbolic manifolds. In all of these three topics, there is a ``soul'' of negative curvature upholding the theory. The volume would make a fine textbook for a graduate-level course
Author : Katsuhiko Matsuzaki
Publisher : Clarendon Press
ISBN 13 : 0191591203
Total Pages : 265 pages
Book Rating : 4.1/5 (915 download)
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 : L. Bers
Publisher : Springer
ISBN 13 : 354037776X
Total Pages : 140 pages
Book Rating : 4.5/5 (43 download)
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 : Irwin Kra
Publisher : Princeton University Press
ISBN 13 : 1400881552
Total Pages : 533 pages
Book Rating : 4.4/5 (8 download)
Download or read book Riemann Surfaces and Related Topics (AM-97), Volume 97 written by Irwin Kra and published by Princeton University Press. This book was released on 2016-03-02 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author : L. Bers
Publisher :
ISBN 13 : 9783662207093
Total Pages : 148 pages
Book Rating : 4.2/5 (7 download)
Download or read book A Crash Course on Kleinian Groups written by L. Bers and published by . This book was released on 2014-01-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : B. Apanasov
Publisher : Springer Science & Business Media
ISBN 13 : 9780792302162
Total Pages : 522 pages
Book Rating : 4.3/5 (21 download)
Download or read book Discrete Groups in Space and Uniformization Problems written by B. Apanasov and published by Springer Science & Business Media. This book was released on 1991-06-30 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
