Hyperbolic Manifolds and Discrete Groups

Author: Michael Kapovich

Publisher: Springer Science & Business Media

ISBN: 9780817639044

Category: Mathematics

Page: 467

View: 3535

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.
Posted in Mathematics

Hyperbolic Manifolds

An Introduction in 2 and 3 Dimensions

Author: Albert Marden

Publisher: Cambridge University Press

ISBN: 1316432521

Category: Mathematics

Page: N.A

View: 2485

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.
Posted in Mathematics

Geometry, Spectral Theory, Groups, and Dynamics

Proceedings in Memory of Robert Brooks, December 29, 2003-January 2, 2004 [and] January 5-9, 2004, Technion-Israel Institute of Technology, Haifa, Israel

Author: Robert Brooks,Michael Entov,Yehuda Pinchover,Michah Sageev

Publisher: American Mathematical Soc.

ISBN: 0821837109

Category: Mathematics

Page: 275

View: 692

This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952-2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and number theory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szegos theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate students and researchers interested in various aspects of geometry and global analysis.
Posted in Mathematics

Lipman Bers, a Life in Mathematics

Author: Linda Keen,Irwin Kra,Rubí E. Rodríguez

Publisher: American Mathematical Soc.

ISBN: 1470420562

Category: Mathematicians

Page: 329

View: 4634

The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis--quasiconformal mappings and moduli of Riemann surfaces--and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grand-students, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time.
Posted in Mathematicians

Complex Kleinian Groups

Author: Angel Cano,Juan Pablo Navarrete,José Seade

Publisher: Springer Science & Business Media

ISBN: 3034804814

Category: Mathematics

Page: 272

View: 9266

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​
Posted in Mathematics

Current Developments in Mathematics

Author: David Jerison,George Lustig,Barry Mazur

Publisher: N.A

ISBN: 9781571461025

Category: Mathematics

Page: 289

View: 1717

Posted in Mathematics

Essays on geometry and related topics

mémoires dédiés à André Haefliger

Author: Étienne Ghys,André Haefliger

Publisher: N.A

ISBN: 9782940264032

Category: Geometry

Page: 610

View: 9995

Posted in Geometry

Geometry & Topology

Author: N.A

Publisher: N.A


Category: Geometry

Page: N.A

View: 6301

Fully refereed international journal dealing with all aspects of geometry and topology and their applications.
Posted in Geometry

Conformal Geometry of Discrete Groups and Manifolds

Author: Boris N. Apanasov

Publisher: Walter de Gruyter

ISBN: 3110808056

Category: Mathematics

Page: 531

View: 8853

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Posted in Mathematics

Indra's Pearls

The Vision of Felix Klein

Author: David Mumford,Caroline Series,David Wright

Publisher: Cambridge University Press

ISBN: 9780521352536

Category: Mathematics

Page: 395

View: 3132

Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry.
Posted in Mathematics

Discrete Groups in Geometry and Analysis

Papers in Honor of G.D. Mostow on His Sixtieth Birthday

Author: Howe

Publisher: Springer Science & Business Media

ISBN: 1489966641

Category: Science

Page: 212

View: 8035

Posted in Science

Essays in Group Theory

Author: S.M. Gersten

Publisher: Springer Science & Business Media

ISBN: 1461395860

Category: Mathematics

Page: 342

View: 1860

Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.
Posted in Mathematics

Geometry and Dynamics of Groups and Spaces

In Memory of Alexander Reznikov

Author: Mikhail Kapranov,Sergii Kolyada,Yu. I. Manin,Pieter Moree,Leonid Potyagailo

Publisher: Springer Science & Business Media

ISBN: 9783764386085

Category: Mathematics

Page: 742

View: 9573

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Posted in Mathematics

A Crash Course on Kleinian Groups

Lectures given at a special session at the January 1974 meeting of the American Mathematical Society at San Francisco

Author: L. Bers,I. Kra

Publisher: Springer

ISBN: 354037776X

Category: Mathematics

Page: 134

View: 7462

Posted in Mathematics