Géométrie Non Commutative

by Alain Connes

Alain Connes, Médaille Fields 1982 et Médaille d'or du CNRS 2004, explore ici les relations existant entre physique théorique et mathématiques. Au terme de sa réflexion, il propose un espace "double" permettant de rendre compte du modèle de Weinberg - Salam, et notamment de l'existence des bosons de Higgs. Un ouvrage véritablement novateur.

Genres: Mathematics, Science

240 pages, Paperback

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.