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. Topology -algebras and theirK-theory862. Elementary Examples of Quotient Spaces903. The SpaceXof Penrose Tilings944.

a countably generated measure space X, the linear space of square-integrable (classes of) measurable functions on X forms a Hilbert space. It is one of the great virtues of the Lebesgue theory that every element of the latter Hilbert space is represented by a measurable function, a fact which easily implies the Radon-Nikodym¶ theorem, for ...

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  Linear, Geometry, Hilbert, Noncommutative, Noncommutative geometry

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