| |
| |
| 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 | |
| |
| |
| Bibliography | |
| |
| |
| Notation and Conventions | |
| |
| |
| Index | |