An Introduction to Manifolds

Authors:

ISBN: 978-0-387-48098-5 (Print) 978-0-387-48101-2 (Online)

Table of contents (28 chapters)

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  1. Front Matter

    Pages i-xviii

  2. Euclidean Spaces

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      Book Chapter

      Pages 5-10

      Smooth Functions on a Euclidean Space

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      Book Chapter

      Pages 11-18

      Tangent Vectors in Rn as Derivations

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      Book Chapter

      Pages 19-32

      Alternating k-Linear Functions

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      Book Chapter

      Pages 33-44

      Differential Forms on Rn

  3. Manifolds

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      Book Chapter

      Pages 47-55

      Manifolds

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      Book Chapter

      Pages 57-62

      Smooth Maps on a Manifold

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      Book Chapter

      Pages 63-74

      Quotients

  4. Lie Groups and Lie Algebras

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      Book Chapter

      Pages 77-89

      The Tangent Space

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      Pages 91-100

      Submanifolds

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      Book Chapter

      Pages 101-104

      Categories and Functors

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      Book Chapter

      Pages 105-117

      The Rank of a Smooth Map

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      Book Chapter

      Pages 119-126

      The Tangent Bundle

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      Book Chapter

      Pages 127-134

      Bump Functions and Partitions of Unity

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      Book Chapter

      Pages 135-146

      Vector Fields

  5. Lie Groups and Lie Algebras

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      Pages 149-160

      Lie Groups

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      Pages 161-171

      Lie Algebras

  6. Differential Forms

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      Book Chapter

      Pages 175-179

      Differential 1-Forms

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      Book Chapter

      Pages 181-188

      Differential k-Forms

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      Book Chapter

      Pages 189-198

      The Exterior Derivative

  7. Integration

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      Book Chapter

      Pages 201-209

      Orientations

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