商品簡介
his book is the English version of the French “Geometrie non commutative” published by InterEditions Paris （1990）. After the excellent initial translation by S.K. Berberian, a considerable amount of rewriting was done and many additions made, multiplying by 3.8 the size of the original manuscript. In particular the present text contains several unpublished results.
目次
TABIF OF CONTENTS
PREFACE
INTRODUCTION
I NONCOMMUTATIVE SPACES AND MEASURE THEORY
1. Heisenberg and the Noncommutative Algebra of Physical Quantities Associated to a Microscopic System
2. Statistical State of a Macroscopic System and Quantum Statistical Mechanics
3. Modular Theory and the Classification of Factors
4. Geometric Examples of yon Neumann Algebras: Measure Theory of Noncommutative Spaces
α Classical Lebesgue measure theory
β. Foliations
γ. The von Neumann algebra of a foliation
5. The Index Theorem for Measured Foliations
α. Transverse measures for follations
β. The Ruelle-Sullivan cycle and the ELder number of a measured foliation
γ. The Index theorem for measured foliations
A. Appendix: Transverse Measures and Averaging Sequences
B. AppendL, c Abstract Transverse Measure Theory
C. Appendix: Noncommutative Spaces and Set Theory
II. TOPOLOGY AND K-THEORY..
1. C*-algebras and their K-theory
2. Elementary Examples of Quotient Spaces
α. Open covers of manifolds
β. The dual of the infinite dihedral group F = Z >~ Z/2
3. The Space X of Penrose Tilings
4. Duals of Discrete Groups and the Novikov Conjecture
5. The Tangent Groupoid of a Manifold
6. Wrong-way Functoriality in K-theory as a Deformation
α. The index groupoid of a linear map
β. Construction off！ ~ E（T*M ~ f*TN, N）
γ. K-orientations of vector bundles and maps
δ. Wrong-way functoriality for K-oriented maps
7. The Orbit Space of a Group Action
8. The Leaf Space of a Foliation
α. Construction of C* （V, F）
β. Closed transversals and idempotents of C* （V, F）
γ. The analytic assembly map/~ : K.,r（BG） -. K（C*（V,F））...
9. The Longitudinal Index Theorem for Foliations
α. Construction of lnd（D） ~ Ko（J）
β. Significance of the C*-algebra Index
γ. The longitudinal index theorem
10. The Analytic Assembly Map and Lie Groups
α. Geometric cycles for smooth groupoids
β. Lie groups and deformations
γ. The G-equivariant index of elliptic operators on homogeneous spaces of Lie groups
δ. The K-theory K （C* （G）） for Lie groups
ε. The general conjecture for smooth groupoids
A. Appendix: C*-modules and Strong Morita Equivalence
B. Appendix: E-theory and Deformations of Algebras
α. Deformations of C*-algebras and asymptotic morphisms
β. Composition of asymptotic morphisms
γ. Asymptotic morphisms and exact sequences of C*-algebras
δ. The cone of a map and half-exactness
ε. E-theory
C. Appendix: Crossed Products of C*-algebras and the Thorn Isomorphism
D. Appendix: Penrose Tilings
III. CYCLIC COHOMOLOGY AND DIFFERENTIAL GEOMETRY
IV. QUANTIZED CALCULUS
V.OPERATOR ALGEBRAS
VI THE METRIC ASPECT OF NONCOMMUTATIVE GEOMETRY
BIBLIOGRAPHY
NOTATION AND CONVENTIONS
INDEX
