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Noncommutative Geometry Alain Connes

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Noncommutative GeometryAlain ConnesContentsPreface6Introduction71. 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 geometry34Chapter 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 4 Appendix D : Penrose Tilings 179 Chapter 3. Cyclic Cohomology and Difierential Geometry 183 1. Cyclic Cohomology 187 2. Examples 212 3.

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