Low-dimensional Topology and Kleinian Groups


Author: D. B. A. Epstein
Publisher: CUP Archive
ISBN: 9780521339056
Category: Mathematics
Page: 321
View: 7105

Continue Reading →

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: 7984

Continue Reading →

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.

Revue de mathématique élémentaires


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 7839

Continue Reading →

Elemente der Mathematik (EL) publishes survey articles about important developments in the field of mathematics; stimulating shorter communications that tackle more specialized questions; and papers that report on the latest advances in mathematics and applications in other disciplines. The journal does not focus on basic research. Rather, its articles seek to convey to a wide circle of readers - teachers, students, engineers, professionals in industry and administration - the relevance, intellectual challenge and vitality of mathematics today. The Problems Section, covering a diverse range of exercises of varying degrees of difficulty, encourages an active grappling with mathematical problems.

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: 7493

Continue Reading →

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: 1643

Continue Reading →

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.

Low-dimensional Geometry

From Euclidean Surfaces to Hyperbolic Knots
Author: Francis Bonahon
Publisher: American Mathematical Soc.
ISBN: 082184816X
Category: Mathematics
Page: 384
View: 7315

Continue Reading →

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.

Hyperbolic Manifolds

An Introduction in 2 and 3 Dimensions
Author: Albert Marden
Publisher: Cambridge University Press
ISBN: 1316432521
Category: Mathematics
Page: N.A
View: 4106

Continue Reading →

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.

Lectures on Block Theory


Author: Burkhard Külshammer
Publisher: Cambridge University Press
ISBN: 9780521405652
Category: Mathematics
Page: 105
View: 9636

Continue Reading →

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

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: 5296

Continue Reading →

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.