Three-Dimensional Geometry and Topology: Volume 1

Three-Dimensional Geometry and Topology: Volume 1

by William P. Thurston
     
 

ISBN-10: 0691083045

ISBN-13: 9780691083049

Pub. Date: 01/17/1997

Publisher: Princeton University Press

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

…  See more details below

Overview

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.

Read More

Product Details

ISBN-13:
9780691083049
Publisher:
Princeton University Press
Publication date:
01/17/1997
Series:
Princeton Mathematical Series
Pages:
320
Product dimensions:
6.52(w) x 9.58(h) x 1.00(d)

Table of Contents


Preface
Reader's Advisory
Ch. 1. What Is a Manifold? 3
Ch. 2. Hyperbolic Geometry and Its Friends 43
Ch. 3. Geometric Manifolds 109
Ch. 4. The Structure of Discrete Groups 209
Glossary 289
Bibliography 295
Index 301

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >