Introduction to Smooth Manifolds

Authors:

ISBN: 978-1-4419-9981-8 (Print) 978-1-4419-9982-5 (Online)

Table of contents (22 chapters)

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  1. Front Matter

    Pages I-XV

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    Book Chapter

    Pages 1-31

    Smooth Manifolds

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    Book Chapter

    Pages 32-49

    Smooth Maps

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    Book Chapter

    Pages 50-76

    Tangent Vectors

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    Book Chapter

    Pages 77-97

    Submersions, Immersions, and Embeddings

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    Book Chapter

    Pages 98-124

    Submanifolds

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    Book Chapter

    Pages 125-149

    Sard’s Theorem

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    Book Chapter

    Pages 150-173

    Lie Groups

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    Book Chapter

    Pages 174-204

    Vector Fields

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    Book Chapter

    Pages 205-248

    Integral Curves and Flows

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    Book Chapter

    Pages 249-271

    Vector Bundles

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    Book Chapter

    Pages 272-303

    The Cotangent Bundle

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    Book Chapter

    Pages 304-326

    Tensors

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    Book Chapter

    Pages 327-348

    Riemannian Metrics

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    Book Chapter

    Pages 349-376

    Differential Forms

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    Book Chapter

    Pages 377-399

    Orientations

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    Book Chapter

    Pages 400-439

    Integration on Manifolds

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    Book Chapter

    Pages 440-466

    De Rham Cohomology

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    Book Chapter

    Pages 467-489

    The de Rham Theorem

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    Book Chapter

    Pages 490-514

    Distributions and Foliations

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    Book Chapter

    Pages 515-539

    The Exponential Map

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