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  • © 1993

Differentiable Manifolds

A First Course

Birkhäuser

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

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  • ISBN: 978-1-4757-2284-0
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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
  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

About this book

"This textbook, probably the best introduction to differential geometry to be published since Eisenhart's, greatly benefits from the author's knowledge of what to avoid, something that a beginner is likely to miss. The presentation is smooth, the choice of topics optimal, and the book can be profitably used for self teaching." --- The Bulletin of Mathematical Books (review of 1st edition)

"A thorough, modern, and lucid treatment of the differential topology, geometry, and global analysis needed to begin advanced study of research in these areas." --- Choice (review of 1st edition)

"Probably the most outstanding novelty...is the appropriate selection of topics." --- Mathematical Reviews (review of 1st edition)

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field.

The themes of linearization, (re) integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further (optional) development of Lie theory than is customary in textbooks at this level. New to this edition is a detailed treatment of covering spaces and the fundamental group.

Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.

Keywords

  • Global Calculus
  • Topology
  • clsmbc
  • differential geometry
  • manifold

Authors and Affiliations

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

    Lawrence Conlon

Bibliographic Information

Buying options

eBook
USD 74.99
Price excludes VAT (USA)
  • ISBN: 978-1-4757-2284-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout