Three-Dimensional Geometry and Topology, Volume 1

by William P. Thurston, Silvio Levy (Editor)

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.

Genres: Mathematics, Geometry

328 pages, Kindle Edition

First published January 17, 1997

Reviews

[Ronald Lett · Rating 5 out of 5]

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.

[Bob Woodley · Rating 5 out of 5]

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.

[Chris · Rating 5 out of 5]

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.

[Jamie · Rating 4 out of 5]

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.