Foundations of Differentiable Manifolds and Lie Groups

Description

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. Front Matter....Pages i-ix Manifolds....Pages 1-52 Tensors and Differential Forms....Pages 53-80 Lie Groups....Pages 81-136 Integration on Manifolds....Pages 137-160 Sheaves, Cohomology, and the de Rham Theorem....Pages 161-217 The Hodge Theorem....Pages 219-258 Back Matter....Pages 259-274