Noncommutative geometry - Connes, Alain (Academic Press, 1994)
Includes bibliographical references (pages 613-644) and index
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. Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Front Cover; Noncommutative Geometry; Copyright Page; TABLE OF CONTENTS; PREFACE; INTRODUCTION; A. Measure theory (Chapters I and V); B. Topology and K-theory (Chapter II); C. Cyclic cohomology (Chapter III); D. The quantized calculus (Chapter IV); E. The metric aspect of noncommutative geometry; CHAPTER I. NONCOMMUTATIVE SPACE AND MEASURE THEORY; I.1. Heisenberg and the Nonconunutative Algebra of Physical Quantities Associated to a Microscopic System; I.2. Statistical State of a Macroscopic System and Quantum Statistical Mechanics; I.3. Modular Theory and the Classification of Factors