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Foundations Of Hyperbolic Manifolds
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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 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.
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 Lectures on Hyperbolic Geometry by : Riccardo Benedetti
Download or read book Lectures on Hyperbolic Geometry written by Riccardo Benedetti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.
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 2001 with total page 500 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 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. This book was released on 2005 with total page 161 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 Hyperbolic Knot Theory by : Jessica S. Purcell
Download or read book Hyperbolic Knot Theory written by Jessica S. Purcell and published by American Mathematical Soc.. This book was released on 2020-10-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.
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 Holomorphic Mappings by : Shoshichi Kobayashi
Download or read book Hyperbolic Manifolds and Holomorphic Mappings written by Shoshichi Kobayashi and published by . This book was released on 1970 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Author :Shoshichi Kobayashi Publisher :World Scientific Publishing Company ISBN 13 :9813101938 Total Pages :161 pages Book Rating :4.8/5 (131 download)
Book Synopsis Hyperbolic Manifolds And Holomorphic Mappings: An Introduction (Second Edition) by : Shoshichi Kobayashi
Download or read book Hyperbolic Manifolds And Holomorphic Mappings: An Introduction (Second Edition) written by Shoshichi Kobayashi and published by World Scientific Publishing Company. This book was released on 2005-11-02 with total page 161 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 Sources of Hyperbolic Geometry by : John Stillwell
Download or read book Sources of Hyperbolic Geometry written by John Stillwell and published by American Mathematical Soc.. This book was released on 1996 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics.
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 Springer. This book was released on 2007-03-11 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Manifolds by : Loring W. Tu
Download or read book An Introduction to Manifolds written by Loring W. Tu and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
