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Foundations of Differentiable Manifolds and Lie Groups

  • Textbook
  • © 1983

Overview

Authors:
  1. Frank W. Warner

    1. Department of Mathematics E1, University of Pennsylvania, Philadelphia, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 94)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
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  2. Manifolds

    • Frank W. Warner
    Pages 1-52

  3. Tensors and Differential Forms

    • Frank W. Warner
    Pages 53-80

  4. Lie Groups

    • Frank W. Warner
    Pages 81-136

  5. Integration on Manifolds

    • Frank W. Warner
    Pages 137-160

  6. Sheaves, Cohomology, and the de Rham Theorem

    • Frank W. Warner
    Pages 161-217

  7. The Hodge Theorem

    • Frank W. Warner
    Pages 219-258

  8. Back Matter

    Pages 259-274
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Keywords

About this book

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find this beginning graduate-level text extremely useful.

Authors and Affiliations

  • Department of Mathematics E1, University of Pennsylvania, Philadelphia, USA

    Frank W. Warner

Bibliographic Information

  • Book Title: Foundations of Differentiable Manifolds and Lie Groups

  • Authors: Frank W. Warner

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1799-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Frank W. Warner 1983

  • Hardcover ISBN: 978-0-387-90894-6Published: 10 October 1983

  • Softcover ISBN: 978-1-4419-2820-7Published: 01 December 2010

  • eBook ISBN: 978-1-4757-1799-0Published: 11 November 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: X, 276

  • Additional Information: Originally published by Scott, Foresman & Company, 1971

  • Topics: Algebra, Manifolds and Cell Complexes (incl. Diff.Topology), Topological Groups, Lie Groups

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