- 可微流形和李群基础(英文版)
- - 作者：Frank W.Warner|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787506266055
  - 出版日期：2004/09/01
  - 页数：272
- 售价：23.6

内容大纲
这本书提供了必要的基础，为学生感兴趣的任何不同领域的数学，需要一个可微歧管的概念。它被设计为一个初级研究生水平的教科书，并假定在代数和分析方面有良好的本科训练，加上一些点集拓扑、覆盖空间和基本群的知识。本书还可作为参考书使用，因为它包含了许多难以从文献中找到的项目，特别是霍奇和德拉姆基本定理的完整和独立的证明。
作者介绍
目录
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
  Orientation
  Integration on Manifolds
  de Rham Cohomology
  Exercises
5  SHEAVES, COHOMOLGY, AND THE DE RHAM THEOREM
  Sheaves and Presheaves
  Cochain Complexes
  Axiomatic Sheaf Cohomology
  The Classical Cohomology Theories
    Alexander-Spanier Cohomology
    de Rham Cohomology
    Singular Cohomology
    Cech Cohomology
  The de Rham Theorem
  Multiplicative Structure
  Supports
  Exercises
6  THE HODGE THEOREM
  The Laplace-Beltrami Operator
  The Hodge Theorem

  Some Calculus
  Elliptic Operators
  Reduction to the Periodic Case
  Ellipticity of the Laplace-Beltrami Operator
  Exercises
BIBLIOGRAPHY
SUPPLEMENT TO BIBLIOGRAPHY
INDEX OF NOTATION
INDEX

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目