可微流形和李群基礎(chǔ)

內(nèi)容概要

This book provides the necessary foundation for students interested in any of the diverse areas of mathematics which require the notion of a differentiable manifold. It is designed as a beginning graduate-level textbook and presumes a good undergraduate training in algebra and analysis plus some knowledge of point set topology, covering spaces, and the fundamental group. It is also intended for use as a reference book since it includes a number of items which are difficult to ferret out of the literature, in particular, thecompleteand self-contained proofs of the fundamental theorems of Hodge and de Rham.

書籍目錄

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　Exercises4 INTEGRATION ON MANIFOLDS5 SHEAVES,COHOMOLGY,AND THE DE RHAM THEOREM6 THE HODGE THEOREMBIBLIOGRAPHYSUPPLEMENT TO BIBLIOGRAPHYINDEX OF NOTATIONINDEX

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