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Author : Riccardo Benedetti,Carlo Petronio
Publisher : Unknown
Page : 348 pages
File Size : 44,7 Mb
Release : 2011-05-13
Category : Electronic
ISBN : 3642581595
Author : Riccardo Benedetti,Carlo Petronio
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581588
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 : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 468 pages
File Size : 40,7 Mb
Release : 2012
Category : Geometry
ISBN : 3037191058
This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master classes in 2008 and 2009. The aim of the master classes was to give fifth-year students and Ph.D. students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were taught by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmuller theory, Lie groups, and asymptotic geometry. The text is aimed at graduate students and research mathematicians. It can also be used as a reference book and as a textbook for short courses on geometry.
Author : Silvio Levy
Publisher : Cambridge University Press
Page : 212 pages
File Size : 55,5 Mb
Release : 1997-09-28
Category : Mathematics
ISBN : 0521629624
Flavors of Geometry is a volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. Growing out of a series of introductory lectures given at the Mathematical Sciences Research Institute in January 1995 and January 1996, the book presents chapters by masters in their respective fields on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation. Each lecture begins with a discussion of elementary concepts, examines the highlights of the field, and concludes with a look at more advanced material. The style and presentation of the chapters are clear and accessible, and most of the lectures are richly illustrated. Bibiliographies and indexes are included to encourage further reading on the topics discussed.
Author : Iskander Asanovich Taĭmanov
Publisher : European Mathematical Society
Page : 224 pages
File Size : 49,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190507
Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. It is addressed to students as well as anyone who wants to learn the basics of differential geometry.
Author : William Goldman
Publisher : World Scientific
Page : 362 pages
File Size : 48,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814401364
This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.
Author : John Roe
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 54,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821833322
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.
Author : Richard Douglas Canary,Albert Marden,D. B. A. Epstein
Publisher : Unknown
Page : 348 pages
File Size : 51,8 Mb
Release : 2014-05-14
Category : Geometry, Hyperbolic
ISBN : 1139126938
Reissued articles from two classic sources on hyperbolic manifolds with new sections describing recent work.
Author : Werner Fenchel
Publisher : Walter de Gruyter
Page : 248 pages
File Size : 49,6 Mb
Release : 1989
Category : Mathematics
ISBN : 3110117347
Hyperbolic geometry is in a period of revised interest. This book contains a substantial account of the parts of the theory basic to the study of Kleinian groups, but it also contains the more broad-reaching thoughts of the author, one of the pioneers in the theory of convex bodies and a major contributor in other fields of mathematics. Annotation copyrighted by Book News, Inc., Portland, OR
Author : D. B. A. Epstein
Publisher : CUP Archive
Page : 340 pages
File Size : 40,9 Mb
Release : 1987-03-19
Category : Mathematics
ISBN : 0521339065
This work and its companion volume form the collected papers from two symposia held at Durham and Warwick in 1984. Volume I contains an expository account by David Epstein and his students of certain parts of Thurston's famous mimeographed notes. This is preceded by a clear and comprehensive account by S. J. Patterson of his fundamental work on measures on limit sets of Kleinian groups.
Author : John Ratcliffe
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 44,9 Mb
Release : 2006-11-25
Category : Mathematics
ISBN : 9780387473222
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 : A. B. Katok,Vaughn Climenhaga
Publisher : American Mathematical Soc.
Page : 307 pages
File Size : 54,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846797
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
Author : R. D. Canary,Albert Marden,D. B. A. Epstein
Publisher : Cambridge University Press
Page : 348 pages
File Size : 52,6 Mb
Release : 2006-04-13
Category : Mathematics
ISBN : 9780521615587
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 : Arlan Ramsay,Robert D. Richtmyer
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 45,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475755855
This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.
Author : Lucian Bădescu
Publisher : Springer Nature
Page : 493 pages
File Size : 51,6 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031514142