Synopses & Reviews
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.
Review:
"A thoroughly modern book on differential geometry... By reason of its thorough treatment of the fundamentals and the two chapters on the de Ram and Hodge theorems, which have not previously had easily accessible proof, [it] certainly fills an unwanted gap in the spectrum of texts." ZENTRALBLATT MATH
Table of Contents
1: Manifolds. 2: Tensor and Differential Forms. 3: Lie Groups. 4: Integration on Manifolds. 5: Sheaves, Cohomology, and the De Rahm Theorem. 6: The Hodge Theorem.
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