| 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 Group Action |
| 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 |
| Quantized Calculus: 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 |
| (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 |
| 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 |
図書
