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    • 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

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