Foundations of Differentiable Manifolds and Lie Groups

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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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.

• Cohomology
• Differenzierbare Mannigfaltigkeit
• Groupssche Gruppe
• Manifolds
• Sheaf cohomology

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

  Frank W. Warner

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