Low-dimensional Topology and Kleinian Groups


Author: D. B. A. Epstein
Publisher: CUP Archive
ISBN: 9780521339056
Category: Mathematics
Page: 321
View: 9530

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Volume 2 is divided into three parts: the first 'Surfaces' contains an article by Thurston on earthquakes and by Penner on traintracks. The second part is entitled 'Knots and 3-Manifolds' and the final part 'Kleinian Groups'.

Differential Topology, Foliations, and Group Actions


Author: Paul A. Schweitzer
Publisher: American Mathematical Soc.
ISBN: 0821851705
Category: Mathematics
Page: 287
View: 7571

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This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions - finite group actions and rigidity theory for Anosov actions - as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.

Four-manifolds, geometries and knots


Author: Jonathan Arthur Hillman,University of Warwick. Mathematics Institute
Publisher: N.A
ISBN: N.A
Category: Four-manifolds (Topology)
Page: 379
View: 803

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Low-dimensional Geometry

From Euclidean Surfaces to Hyperbolic Knots
Author: Francis Bonahon
Publisher: American Mathematical Soc.
ISBN: 082184816X
Category: Mathematics
Page: 384
View: 4730

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The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

Geometry of Low-Dimensional Manifolds: Volume 2

Symplectic Manifolds and Jones-Witten Theory
Author: Donaldson/Thomas,London Mathematical Society
Publisher: Cambridge University Press
ISBN: 9780521400015
Category: Mathematics
Page: 260
View: 7764

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These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.

Hyperbolic Manifolds

An Introduction in 2 and 3 Dimensions
Author: Albert Marden
Publisher: Cambridge University Press
ISBN: 1316432521
Category: Mathematics
Page: N.A
View: 4052

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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.

Discrete Groups and Geometry


Author: Conference on discrete groups and geometry,W. J. Harvey
Publisher: Cambridge University Press
ISBN: 9780521429320
Category: Mathematics
Page: 248
View: 2913

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This volume contains a selection of refereed papers presented in honour of A.M. Macbeath, one of the leading researchers in the area of discrete groups. The subject has been of much current interest of late as it involves the interaction of a number of diverse topics such as group theory, hyperbolic geometry, and complex analysis.

Lectures on Block Theory


Author: Burkhard Külshammer
Publisher: Cambridge University Press
ISBN: 9780521405652
Category: Mathematics
Page: 105
View: 5432

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This textbook is intended as a self contained introduction into that part of algebra known as representation of finite groups.