可微流形和李群基礎

內容簡介

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.

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

可微流形和李群基礎

基本介紹

內容簡介

目錄

相關詞條

熱門詞條