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Birkhäuser

Differentiable Manifolds

A First Course

  • Book
  • © 1993

Overview

Authors:
  1. Lawrence Conlon

    1. Department of Mathematics, Washington University, St. Louis, USA

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Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Topological Manifolds

    • Lawrence Conlon
    Pages 1-24

  3. The Local Theory of Smooth Functions

    • Lawrence Conlon
    Pages 25-66

  4. The Global Theory of Smooth Functions

    • Lawrence Conlon
    Pages 67-100

  5. Flows and Foliations

    • Lawrence Conlon
    Pages 101-125

  6. Lie Groups and Lie Algebras

    • Lawrence Conlon
    Pages 127-157

  7. Covectors and 1—Forms

    • Lawrence Conlon
    Pages 159-187

  8. Multilinear Algebra and Tensors

    • Lawrence Conlon
    Pages 189-220

  9. Integration of Forms and de Rham Cohomology

    • Lawrence Conlon
    Pages 221-276

  10. Forms and Foliations

    • Lawrence Conlon
    Pages 277-292

  11. Riemannian Geometry

    • Lawrence Conlon
    Pages 293-348

  12. Back Matter

    Pages 349-395
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Keywords

About this book

This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen­ tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non­ linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result­ ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.

Authors and Affiliations

  • Department of Mathematics, Washington University, St. Louis, USA

    Lawrence Conlon

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