Kleinian Groups And Hyperbolic 3 Manifolds

Author : Katsuhiko Matsuzaki
Publisher : Clarendon Press
ISBN 13 : 0191591203
Total Pages : 265 pages
Book Rating : 4.04/5 ( download)

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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 : Y. Komori
Publisher : Cambridge University Press
ISBN 13 : 9781139437233
Total Pages : 396 pages
Book Rating : 4.32/5 ( download)

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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 : A. Marden
Publisher : Cambridge University Press
ISBN 13 : 1139463764
Total Pages : 393 pages
Book Rating : 4.68/5 ( download)

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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 : 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 : 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 : William P. Thurston
Publisher : American Mathematical Society
ISBN 13 : 1470474743
Total Pages : 337 pages
Book Rating : 4.44/5 ( download)

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Download or read book The Geometry and Topology of Three-Manifolds written by William P. Thurston and published by American Mathematical Society. This book was released on 2023-06-16 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.

Author : Y. Komori
Publisher :
ISBN 13 : 9780511180248
Total Pages : 394 pages
Book Rating : 4.41/5 ( download)

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Download or read book Kleinian Groups and Hyperbolic 3-Manifolds written by Y. Komori and published by . This book was released on 2003 with total page 394 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 conje.

Author : Yair N. Minsky
Publisher : Cambridge University Press
ISBN 13 : 1139447211
Total Pages : 399 pages
Book Rating : 4.18/5 ( download)

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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 : Y. Komori
Publisher : Cambridge University Press
ISBN 13 : 9780521540131
Total Pages : 392 pages
Book Rating : 4.35/5 ( download)

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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 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including presentations by field authorities describing the state of current research, a workshop was held on Kleinian groups and hyperbolic 3-manifolds in September 2001. This volume includes a selection of workshop contributions representative of its extremely high standards. Beginning graduate students will find them inspiring, and established researchers will discover reliable references to current research.

Author : Richard Douglas Canary
Publisher : American Mathematical Soc.
ISBN 13 : 9780821865347
Total Pages : 244 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Homotopy Equivalences of 3-manifolds and Deformation Theory of Kleinian Groups written by Richard Douglas Canary and published by American Mathematical Soc.. This book was released on 2004-09-23 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text investigates a natural question arising in the topological theory of $3$-manifolds, and applies the results to give new information about the deformation theory of hyperbolic $3$-manifolds. It is well known that some compact $3$-manifolds with boundary admit homotopy equivalences that are not homotopic to homeomorphisms. We investigate when the subgroup $\mathcal{R}(M)$ of outer automorphisms of $\pi_1(M)$ which are induced by homeomorphisms of a compact $3$-manifold $M$ has finite index in the group $\operatorname{Out}(\pi_1(M))$ of all outer automorphisms. This question is completely resolved for Haken $3$-manifolds. It is also resolved for many classes of reducible $3$-manifolds and $3$-manifolds with boundary patterns, including all pared $3$-manifolds. The components of the interior $\operatorname{GF}(\pi_1(M))$ of the space $\operatorname{AH}(\pi_1(M))$ of all (marked) hyperbolic $3$-manifolds homotopy equivalent to $M$ are enumerated by the marked homeomorphism types of manifolds homotopy equivalent to $M$, so one may apply the topological results above to study the topology of this deformation space. We show that $\operatorname{GF}(\pi_1(M))$ has finitely many components if and only if either $M$ has incompressible boundary, but no ``double trouble,'' or $M$ has compressible boundary and is ``small.'' (A hyperbolizable $3$-manifold with incompressible boundary has double trouble if and only if there is a thickened torus component of its characteristic submanifold which intersects the boundary in at least two annuli.) More generally, the deformation theory of hyperbolic structures on pared manifolds is analyzed. Some expository sections detail Johannson's formulation of the Jaco-Shalen-Johannson characteristic submanifold theory, the topology of pared $3$-manifolds, and the deformation theory of hyperbolic $3$-manifolds. An epilogue discusses related open problems and recent progress in the deformation theory of hyperbolic $3$-manifolds.