Foundations Of Hyperbolic Manifolds

Author : John Ratcliffe
Publisher : Springer Science & Business Media
ISBN 13 : 1475740131
Total Pages : 761 pages
Book Rating : 4.34/5 ( download)

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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.

Author : John G. Ratcliffe
Publisher : Springer Nature
ISBN 13 : 3030315975
Total Pages : 800 pages
Book Rating : 4.79/5 ( download)

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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.

Author : John Ratcliffe
Publisher : Springer
ISBN 13 : 9780387512969
Total Pages : 0 pages
Book Rating : 4.69/5 ( download)

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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.

Author : R. D. Canary
Publisher : Cambridge University Press
ISBN 13 : 9781139447195
Total Pages : 356 pages
Book Rating : 4.9X/5 ( download)

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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.

Author : Michael Kapovich
Publisher : Springer Science & Business Media
ISBN 13 : 0817649131
Total Pages : 470 pages
Book Rating : 4.35/5 ( download)

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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.

Author : R. D. Canary
Publisher : Cambridge University Press
ISBN 13 : 0521615585
Total Pages : 348 pages
Book Rating : 4.87/5 ( download)

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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 348 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.

Author : Colin Maclachlan
Publisher : Springer Science & Business Media
ISBN 13 : 147576720X
Total Pages : 472 pages
Book Rating : 4.09/5 ( download)

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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

Author : Riccardo Benedetti
Publisher : Springer Science & Business Media
ISBN 13 : 3642581587
Total Pages : 343 pages
Book Rating : 4.88/5 ( download)

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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.

Author : Albert Marden
Publisher : Cambridge University Press
ISBN 13 : 1316432521
Total Pages : 535 pages
Book Rating : 4.25/5 ( download)

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Download or read book Hyperbolic Manifolds written by Albert Marden and published by Cambridge University Press. This book was released on 2016-02-01 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.

Author : Richard Douglas Canary
Publisher :
ISBN 13 : 9781139126939
Total Pages : 348 pages
Book Rating : 4.38/5 ( download)

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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.