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. The Index Theorem for Measured Foliations64 Appendix A : Transverse Measures and Averaging Sequences77 Appendix B : Abstract Transverse Measure Theory78 Appendix C : Noncommutative Spaces and Set Theory79 chapter 2.
Contents Preface 6 Introduction 7 1. Measure theory (Chapters I and V) 8 2. Topology and K-theory (Chapter II) 14 3. Cyclic cohomology (Chapter III) 19 4. The quantized calculus (Chapter IV) 25
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