William P. Thurston's Books

Three-dimensional Geometry and Topology

By: William P. Thurston

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Three-dimensional Geometry and Topology

By: William P. Thurston

Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.

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Page Count

340

Publisher

Princeton University Press

Published Date

ISBN 10

0691083045

ISBN 13

9780691083049

Confoliations

By: Y. Eliashberg,William P. Thurston

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Confoliations

By: Y. Eliashberg,William P. Thurston

This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Developing almost independently, these theories at first glance belonged to two different worlds: The theory of foliations is part of topology and dynamical systems, while contact geometry is the odd-dimensional "brother" of symplectic geometry. However, both theories have developed a number of striking similarities. Confoliations--which interpolate between contact structures and codimension-one foliations--should help us to understand better links between the two theories. These links provide tools for transporting results from one field to the other.

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821807765

ISBN 13

9780821807767

The Geometry and Topology of Three-Manifolds

With a Preface by Steven P. Kerckhoff

By: William P. Thurston

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The Geometry and Topology of Three-Manifolds

With a Preface by Steven P. Kerckhoff

By: William P. Thurston

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.

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Page Count

338

Publisher

American Mathematical Society

Published Date

ISBN 10

1470463911

ISBN 13

9781470463915

Three-Dimensional Geometry and Topology, Volume 1

(PMS-35)

By: William P. Thurston

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Three-Dimensional Geometry and Topology, Volume 1

(PMS-35)

By: William P. Thurston

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

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Page Count

323

Publisher

Princeton University Press

Published Date

ISBN 10

1400865328

ISBN 13

9781400865321

Wonders of the World

By: Ronald William Clark

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Wonders of the World

By: Ronald William Clark

Looks at more than fifty of the world's natural and man-made wonders from the Grand Canyon and stress patterns in metal to Machu Picchu and the space-shuttle.

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Page Count

104

Published Date

ISBN 10

0668049324

ISBN 13

9780668049320

The Geometry and Topology of Three-Manifolds

With a Preface by Steven P. Kerckhoff

By: William P. Thurston

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The Geometry and Topology of Three-Manifolds

With a Preface by Steven P. Kerckhoff

By: William P. Thurston

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Solve jigsaw puzzle

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Page Count

338

Publisher

American Mathematical Society

Published Date

ISBN 10

1470463911

ISBN 13

9781470463915

Book's by William P. Thurston

Three-dimensional Geometry and Topology

Three-dimensional Geometry and Topology

Confoliations

Confoliations

The Geometry and Topology of Three-Manifolds

The Geometry and Topology of Three-Manifolds

Three-Dimensional Geometry and Topology, Volume 1

Three-Dimensional Geometry and Topology, Volume 1

Wonders of the World

Wonders of the World

The Geometry and Topology of Three-Manifolds

The Geometry and Topology of Three-Manifolds

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