Noncommutative Geometry

by Alain Connes

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.

Genres: Mathematics, Science

680 pages, Hardcover

First published January 1, 1990

Reviews

[Jon Paprocki · Rating 4 out of 5]

This book has been on my shelf for several years. It is more of a bible for noncommutative geometry written by its chief inventor than it is a math textbook. If you want the perspective and context that Alain Connes invented all of these crazy ideas in, this is the first place to go. It does not necessarily provide the best explanation on every topic in contemporary noncommutative geometry, but to truly understand a topic you must know what motivated its development at every step of the way, and for that this book is completely essential. What really makes this book unique among research level mathematics texts is the fact that proofs are scarce! Proofs are generally only given if they are both short and insightful.

For somebody who is new to noncommutative geometry, though, I don't think this book is needed immediately. The lengthy survey A Walk in the Noncommutative Garden by Connes and Marcolli suffices as a first introduction, and then I would move to Elements of Noncommutative Geometry by Gracia-Bondia, Varilly, and Figueroa to get into the meat.