What do you think?
Rate this book
Three-Dimensional Geometry and Topology, Vol. 1
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.
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.
- GenresMathematicsGeometry
328 pages, Hardcover
First published January 17, 1997
3 people are currently reading
147 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 4 of 4 reviews
December 12, 2011
This book is an unequalled treasure of 3-dimensional topology. It contains both physical model challenges to engage the abstraction of topology with the physical world and extremely insightful abstract discussions and exercises for the reader. This is not something that you can read from beginning to ending; rather you can pick it up and read any chapter and come away brimming with ideas and investigations. Excellent text written by an accomplished expert in the field (a well-deserved Field's Medal and another AMS award for this book alone!). This means you will be getting the raw new theorems and constructions (they comprise a large enough region of modern math to be known as "Thurston-type geometry") communicated directly from the original creator who sweated over and divined them for the first time.
While reading this text, you get the feeling that you are in the presence of someone who is not only completely immersed in his topic and its context in the larger picture, but that he enjoys illuminating all of it for you.
For undergraduates, be sure you are well-versed in basic topology before engaging this text for the best learning experience.
While reading this text, you get the feeling that you are in the presence of someone who is not only completely immersed in his topic and its context in the larger picture, but that he enjoys illuminating all of it for you.
For undergraduates, be sure you are well-versed in basic topology before engaging this text for the best learning experience.
January 2, 2019
This is perhaps one of the most amazing books on my bookshelf. The topics are quite advanced and the explanations are fast moving. I generally read a few pages of this book and then I realize I need to fill in some gaps in my understanding. So I read several others texts and then return to this book with a greater understanding and start again. I've reread the first chapter many times.
It is clear that the author was a genius who spent considerable effort trying to write the most lucid text possible explaining extremely abstract and difficult concepts. To some extent it is a survey text; it covers a wide field, thus he moves quickly and writes succinctly.
Thurston did so much ground-breaking work in this field that you could say he created it himself. The fact that he labored to communicate clearly is a gift to us. The flashes of genius that are revealed are the reward for the effort required.
It is clear that the author was a genius who spent considerable effort trying to write the most lucid text possible explaining extremely abstract and difficult concepts. To some extent it is a survey text; it covers a wide field, thus he moves quickly and writes succinctly.
Thurston did so much ground-breaking work in this field that you could say he created it himself. The fact that he labored to communicate clearly is a gift to us. The flashes of genius that are revealed are the reward for the effort required.
January 1, 2019
6/5
One of the best books I've ever read.
Makes my list of "if I could force middle and high school math students to read…�"
Non-mathematicians: it will change what you think mathematics is about, and make you think. For example flip to chapter 8, orbifolds. You will understand his points, because his writing is that clear.
One of the best books I've ever read.
Makes my list of "if I could force middle and high school math students to read…�"
Non-mathematicians: it will change what you think mathematics is about, and make you think. For example flip to chapter 8, orbifolds. You will understand his points, because his writing is that clear.
December 2, 2012
Thurston is a genius and a good writer. Highly recommended, though I never made it past the first couple chapters. I hope to pick it up again someday.
Displaying 1 - 4 of 4 reviews
Can't find what you're looking for?
Get help and learn more about the design.