| 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 Ext... |
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