
Noncommutative Geometry (Hardback)
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Dispatched in 2 business days When will my order arrive?  DescriptionThis English version of the pathbreaking 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. It includes features such as: first full treatment of the subject and its applications; written by the pioneer of this field; broad applications in mathematics; of interest across most fields; ideal as an introduction and survey; examples treated include: @subbul; the space of Penrose tilings; the space of leaves of a foliation; the space of irreducible unitary representations of a discrete group; the phase space in quantum mechanics; the Brillouin zone in the quantum Hall effect; and a model of space time.
 Publisher: Academic Press Inc
 Published: 17 January 1995
 Format: Hardback 661 pages
 See: Full bibliographic data
 Categories: Algebra  Functional Analysis & Transforms  Differential Calculus & Equations  Geometry  Algebraic Geometry  Topology  Physics  Particle & Highenergy Physics  Mathematical Physics
 ISBN 13: 9780121858605 ISBN 10: 012185860X
 Sales rank: 754,232
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Full bibliographic data for Noncommutative Geometry
 Title
 Noncommutative Geometry
 Authors and contributors
 Physical properties
 Format: Hardback
Number of pages: 661
Width: 178 mm
Height: 258 mm
Thickness: 34 mm
Weight: 1,302 g  Language
 English
 ISBN
 ISBN 13: 9780121858605
ISBN 10: 012185860X  Classifications
BIC E4L: MAT
Nielsen BookScan Product Class 3: S7.8
B&T Book Type: NF
B&T Modifier: Region of Publication: 01
B&T General Subject: 710
B&T Modifier: Academic Level: 02
B&T Merchandise Category: POD
Ingram Subject Code: MA
Libri: IMA
BIC subject category V2: PBF, PBP
BISAC V2.8: SCI055000
WarengruppenSystematik des deutschen Buchhandels: 16240
BIC subject category V2: PBKF
BISAC V2.8: MAT012000
BIC subject category V2: PBKJ
BISAC V2.8: MAT002050, MAT007000
BIC subject category V2: PHP
BISAC V2.8: SCI040000
BIC subject category V2: PBMW
DC22: 516.3/5
LC classification: QA564 .C6713 1994
LC subject heading: ,
B&T Approval Code: A51602400
DC22: 516.35
LC subject heading: ,
DC20: 516.35
LC classification: QA564.C671
BISAC V2.8: MAT012010
Thema V1.0: PHP, PBF, PBMW, PBKF, PBP Illustrations note
 references, indices
 Publisher
 Elsevier Science Publishing Co Inc
 Imprint name
 Academic Press Inc
 Publication date
 17 January 1995
 Publication City/Country
 San Diego
 Table of 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 KTheory: C*Algebras and their KTheory. 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. Wrongway Functionality in KTheory 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 KTheory. The Higher Index Theorem for Covering Spaces. The Novikov Conjecture for Hyperbolic Groups. Factors of Type III, Cyclic Cohomology and the GodbillonVey 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 RankOne 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 KCycles, 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 RadonNikodom 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 YangMills 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 KTheory. Cyclic Cohomology and Differential Geometry. Quantized Calculus. Operator Algebras. The Metric Aspect of Noncommutative Geometry. Bibliography. Notation and Conventions. Index.