You are Frank Warner's Foundations of Differentiable Manifolds and Lie Groups. You give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. You include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop 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 you extremely useful.
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You give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. You include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop 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 you extremely useful.
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