Format:
Online-Ressource (678 p.)
Edition:
Online-Ausg. 2011 Electronic reproduction; Available via World Wide Web
ISBN:
9780121858605
Content:
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
Note:
Description based upon print version of record
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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
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I.4. Geometric Examples of von Neumann Algebras: Measure Theory of Noncommutative SpacesI.5. The Index Theorem for Measured Foliations; I. Appendix A. Transverse Measures and Averaging Sequences; I. Appendix B. Abstract Transverse Measure Theory; I. Appendix C. Noncommutative Spaces and Set Theory; CHAPTER II. TOPOLOGY AND K-THEORY; II.1. C*-algebras and their K-theory; II.2. Elementary Examples of Quotient Spaces; II.3. The Space X of Penrose Tilings; II.4. Duals of Discrete Groups and the Novikov Conjecture; II.5. The Tangent Groupoid of a Manifold
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II.6. Wrong-way Functoriality in K-theory as a DeformationII.7. The Orbit Space of a Group Action; II.8. The Leaf Space of a Foliation; II.9. The Longitudinal Index Theorem for Foliations; II.10. The Analytic Assembly Map and Lie Groups; II. Appendix A. C* -modules and Strong Morita Equivalence; II. Appendix B. E-theory and Deformations of Algebras; II. Appendix C. Crossed Products of C*-algebras and the Thom Isomorphism; II. Appendix D. Penrose Tilings; CHAPTER III. CYCLIC COHOMOLOGY AND DIFFERENTIAL GEOMETRY; III.1. Cyclic Cohomology; III.2. Examples
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III.3. Pairing of Cyclic Cohomology with K-TheoryIII.4. The Higher Index Theorem for Covering Spaces; III.5. The Novikov Conjecture for Hyperbolic Groups; III.6. Factors of Type III, Cyclic Cohomology and the Godbillon-Vey Invariant; III.7. The Transverse Fundamental Class for Foliations and Geometric Corollaries; III. Appendix A. The Cyclic Category A; III. Appendix B. Locally Convex Algebras; III. Appendix C. Stability under Holomorphic Functional Calculus; CHAPTER IV. QUANTIZED CALCULUS; IV.1. Quantized Differential Calculus and Cyclic Cohomology
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IV.2. The Dixmier Trace and the Hochschild Class of the CharacterIV.3. Quantized Calculus in One Variable and Fractal Sets; IV.4. Conformal Manifolds; IV.5. Fredholm Modules and Rank-One Discrete Groups; IV.6. Elliptic Theory on the Noncommutative Torus T2θ and the Quantum Hall Effect; IV.7. Entire Cyclic Cohomology; IV.8. The Chern Character of θ-summable Fredholm Modules; IV.9. θ-summable K-cycles, Discrete Groups and Quantum Field Theory; IV. Appendix A. Kasparov's Bivariant Theory; IV. Appendix B. Real and Complex Interpolation of Banach Spaces
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IV. Appendix C. Normed Ideals of Compact Operators
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Electronic reproduction; Available via World Wide Web
Additional Edition:
9780080571751
Additional Edition:
Print version Noncommutative Geometry
Language:
English
Keywords:
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