非交换微分几何及其在物理学中的应用导论

1 Introduction

2 Differential Geometry

2.1 Diiferential manifolds

2.2 Metrics and connections

2.3 Cohomology

3 Matrix Geometry

3.1 Differential forms I

3.2 Differential forms II

3.3 Tensor products

3.4 Metrics

3.5 Yang-Mills connections

3.6 Linear connections

3.7 Curvature

4 Noncommutative Geometry

4.1 General algebras

4.2 Poisson structures

4.3 Topological algebras

4.4 Quantum groups

5 Vector Bundles

5.1 K-theory

5.2 A matrix analogue

5.3 Predholm modules

6 Cyclic Homology

6.1 The universal calculus

6.2 Cyclic homology

6.3 Morita equivalence

6.4 The Loday-QuiUen theorem

7 Modifications of Space-Time

7.1 Noncommutative space-time

7.2 A finite model

7.3 Fuzzy physics

8 Extensions of Space-Time

8.1 The spinning particle

8.2 Noncommutative electrodynamics

8.3 Modified Kaluza-Klein theory

《非交换微分几何及其在物理学中的应用导论（第2版）》主要内容包括了Differential forms I、Differential forms II、Tensor products、Metrics、Yang-Mills connections、Linear connections、Curvature等。