Transcription of Noncommutative Geometry Alain Connes
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Noncommutative Geometry Alain Connes
Noncommutative GeometryAlain ConnesContentsPreface6 Introduction71. Measure theory (Chapters I and V)82. Topology andK-theory (Chapter II)143. Cyclic cohomology (Chapter III)194. The quantized calculus (Chapter IV)255. The metric aspect of Noncommutative geometry34 Chapter 1. Noncommutative Spaces and Measure Theory391. Heisenberg and the Noncommutative Algebra of Physical Quantities402. Statistical State of a Macroscopic System and Quantum StatisticalMechanics453. Modular Theory and the Classification of Factors484. Geometric Examples of von Neumann Algebras : Measure Theory ofNoncommutative Spaces515.
CONTENTS 5 Appendix A. Crossed Products of von Neumann Algebras 537 Appendix B. Correspondences 539 Chapter 6. The metric aspect of noncommutative geometry 552
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