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.

9. The Longitudinal Index Theorem for Foliations 134 10. The Analytic Assembly Map and Lie Groups 141 Appendix A : C⁄-modules and Strong Morita Equivalence 156 Appendix B : E-theory and Deformations of Algebras 163 Appendix C : Crossed Products of C⁄-algebras and the Thom Isomorphism 175 3

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  Index, Geometry, Theorem, Longitudinal, Longitudinal index theorem for foliations, Foliations, Noncommutative, Noncommutative geometry

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