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| NONCOMMUTATIVE GEOMETRY
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By
Alain Connes, IHES
Description
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to
measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book
is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics,
quantization, and elementary particles and fields.
Audience
Graduate students and researchers in mathematics and mathematical physics. Particular appeal for analysts, geometers, and differential
geometers; those interested in quantization in physics and mathematics; particle physicists,functional analysts; and algebraists.
Contents
Noncommutative Spaces and Measure Theory:
Heisenberg and the Noncommutative Algebra of Physical Quantities Associated
to a Microscopic System. Statistical State of a Macroscopic System and Quantum Statistical Mechanics. Modular Theory and the Classification
of Factors. Geometric Examples of von Neumann Algebras: Measure Theory of Noncommutative Spaces. The Index Theorem for Measured Foliations.
Topology and K
-Theory: C*-Algebras and their K-Theory. Elementary Examples of Quotient
Spaces. The Space X of Penrose Tilings. Duals of Discrete Groups and the Novikov Conjecture. The Tangent Groupoid of a Manifold.
Wrong-way Functionality in K-Theory as a Deformation. The Orbit Space of a GroupAction. The Leaf Space of a Foliation. The Longitudinal
Index Theorem for Foliations. The Analytic Assembly Map and Lie Groups.
Cyclic Cohomology and Differential Geometry:
Cyclic Cohomology. Examples. Pairing of Cyclic Cohomology with K-Theory. The Higher Index Theorem for Covering Spaces. The Novikov
Conjecture for Hyperbolic Groups. Factors of Type III, Cyclic Cohomology and the Godbillon-Vey Invariant. The Transverse Fundamental
Class for Foliations and Geometric Corollaries.
QuantizedCalculus:
Quantized Differential Calculus and Cyclic Cohomology.
The Dixmier Trace and the Hochschild Class of the Character. Quantized Calculus in One Variable and Fractal Sets. Conformal Manifolds.
Fredholm Modules and Rank-One Discrete Groups. Elliptic Theory on the Noncommutative Torus (NOTE: See book for proper symbol. Math T
with a 2 over () and the Quantum Hall Effect. Entire Cyclic Cohomology. The Chern Character of (-Summable Fredholm Modules. (-Summable K-Cycles, Discrete Groups, and Quantum Field Theory.
Operator Algebras:
The Papers of Murray
and von Neumann. Representations of C*-Algebras. The Algebraic Framework for Noncommutative Integration and the Theory of Weights.
The Factors of Powers, Araki and Woods,and of Krieger. The Radon-Nikodom Theorem and Factors of Type III(. Noncommutative Ergodic Theory.
Amenable von Neumann Algebras. The Flow of Weights: mod(M). The Classification of Amenable Factors. Subfactors of Type II1 Factors.
Hecke Algebras ,Type III Factors and Statistical Theory of Prime Numbers.
The Metric Aspect of Noncommutative Geometry:
Riemannian Manifolds and the Dirac Operator. Positivity in Hochschild Cohomology and the Inequalities for the Yang-Mills Action. Product
of the Continuum by the Discrete and the Symmetry Breaking Mechanism. The Notion of Manifold in Noncommutative Geometry. The Standard U (1) x SU (2) x SU (3) Model. Bibliography. Notation and Conventions. Index.CONTENTS (Chapter Headings):
Noncommutative Spaces and Measure Theory. Topology and K-Theory. Cyclic Cohomology and Differential Geometry. Quantized Calculus.
Operator Algebras. The Metric Aspect of Noncommutative Geometry. Bibliography. Notation and Conventions. Index.
| Bibliographic details |
Hardbound, 661 pages, publication date: NOV-1994
ISBN-13: 978-0-12-185860-5
ISBN-10: 0-12-185860-X
Imprint: ACADEMIC PRESS
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| Price and Ordering |
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EUR 92.95
USD 128
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Last update: 4 Sep 2009
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