| 1 MANIFOLDS Preliminaries Differentiable Manifolds The Second Axiom of Countability Tangent Vectors and Differentials Submanifolds， Diffeomorphisms， and the Inverse Function Theorem Implicit Function Theorems Vector Fields Distributions and the Frobenius Theorem Exercises 2 TENSORS AND DIFFERENTIAL FORMS Tensor and Exterior Algebras Tensor Fields and Differential Forms The Lie Derivative Differential Ideals Exercises 3 IE GROUPS Lie Groups and Their Lie Algebras Homomorphisms Lie Subgroups Coverings Simply Connected Lie Groups Exponential Map Continuous Homomorphisms Closed Subgroups The Adjoint Representation Automorphisms and Derivations of Bilinear Operations and Forms Homgeneous Manifolds Exercises 4 INTEGRATION ON MANIFOLDS 5 SHEAVES,COHOMOLGY,AND THE DE RHAM THEOREM 6 THE HODGE THEOREM BIBLIOGRAPHY SUPPLEMENT TO BIBLIOGRAPHY INDEX OF NOTATION INDEX |
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