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Fundamentals Of Hyperbolic Manifolds
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Book Synopsis Fundamentals of Hyperbolic Manifolds by : R. D. Canary
Download or read book Fundamentals of Hyperbolic Manifolds written by R. D. Canary and published by Cambridge University Press. This book was released on 2006-04-13 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.
Book Synopsis Foundations of Hyperbolic Manifolds by : John Ratcliffe
Download or read book Foundations of Hyperbolic Manifolds written by John Ratcliffe and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.
Book Synopsis Foundations of Hyperbolic Manifolds by : John G. Ratcliffe
Download or read book Foundations of Hyperbolic Manifolds written by John G. Ratcliffe and published by Springer Nature. This book was released on 2019-10-23 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.
Book Synopsis Fundamentals of Hyperbolic Geometry by : Richard Douglas Canary
Download or read book Fundamentals of Hyperbolic Geometry written by Richard Douglas Canary and published by . This book was released on 2014-05-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reissued articles from two classic sources on hyperbolic manifolds with new sections describing recent work.
Book Synopsis Hyperbolic Manifolds by : Albert Marden
Download or read book Hyperbolic Manifolds written by Albert Marden and published by Cambridge University Press. This book was released on 2016-02 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.
Book Synopsis Hyperbolic Manifolds and Discrete Groups by : Michael Kapovich
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.
Book Synopsis The Arithmetic of Hyperbolic 3-Manifolds by : Colin Maclachlan
Download or read book The Arithmetic of Hyperbolic 3-Manifolds written by Colin Maclachlan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise way; At present no such text exists
Book Synopsis Hyperbolic Manifolds and Kleinian Groups by : Katsuhiko Matsuzaki
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.
Book Synopsis Foundations of Hyperbolic Manifolds by : John Ratcliffe
Download or read book Foundations of Hyperbolic Manifolds written by John Ratcliffe and published by Springer. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.
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 :Shoshichi Kobayashi Publisher :World Scientific Publishing Company ISBN 13 :9813101938 Total Pages :160 pages Book Rating :4.8/5 (131 download)
Book Synopsis Hyperbolic Manifolds and Holomorphic Mappings by : Shoshichi Kobayashi
Download or read book Hyperbolic Manifolds and Holomorphic Mappings written by Shoshichi Kobayashi and published by World Scientific Publishing Company. This book was released on 2005-11-02 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
Book Synopsis The Hyperbolization Theorem for Fibered 3-Manifolds by : Jean-Pierre Otal
Download or read book The Hyperbolization Theorem for Fibered 3-Manifolds written by Jean-Pierre Otal and published by American Mathematical Soc.. This book was released on 2001 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students familiar with low-dimensional topology and researchers in geometry and topology, Otal (CNRS-UMR 128, Lyon) offers a complete proof of Thurston's hyperbolization theorem for 3-manifolds that fiber as surface bundles. The original Le Theoreme d'Hyperbolisation pour les Varietes de Dimension 3, published by the French Mathematical Society in 1996, has been translated by Leslie D. Kay. c. Book News Inc.
Book Synopsis Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds by : Alexander Isaev
Download or read book Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds written by Alexander Isaev and published by Lecture Notes in Mathematics. This book was released on 2007-02-09 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.
Book Synopsis Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 by : Curtis T. McMullen
Download or read book Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 written by Curtis T. McMullen and published by Princeton University Press. This book was released on 2014-09-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Book Synopsis Normally Hyperbolic Invariant Manifolds in Dynamical Systems by : Stephen Wiggins
Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.
Book Synopsis Flat Manifolds Appearing as Cusps of Hyperbolic Manifolds by : Barbara Ellen Nimershiem
Download or read book Flat Manifolds Appearing as Cusps of Hyperbolic Manifolds written by Barbara Ellen Nimershiem and published by . This book was released on 1992 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Differential Geometry by : Serge Lang
Download or read book Fundamentals of Differential Geometry written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
