Titlebook: Differentiable Manifolds; Lawrence Conlon Textbook 2001Latest edition Birkh?user Boston 2001 Differential Geometry.Global Calculus.Topolog

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Topological Manifolds,This chapter pertains to the global theory of manifolds. See also [., Chapter I] and [., Chapter 1].

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The Global Theory of Smooth Functions,Our present goal is to extend the theory of smooth functions, developed on open subsets of ?. in Chapter 2, to arbitrary differentiable manifolds. Geometric topology becomes an essential feature.

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Lie Groups and Lie Algebras,Lie groups and their Lie algebras play a central role in geometry, topology, and analysis. Here we can only give a brief introduction to this fascinating topic.

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Multilinear Algebra and Tensors,Smooth functions, vector fields and 1-forms are . of fairly simple types. In order to handle higher order tensors, we will need some rather sophisticated multilinear algebra. The reader who is well grounded in the multilinear algebra of .-modules can skip ahead to Section 7.4, referring to the first three sections only as needed.

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Forms and Foliations,In Section 4.5, we proved the vector field version of the Frobenius integrability theorem: . Γ(.) .(.) .. In this chapter, we develop an equivalent version of this theorem, stated in terms of the Grassmann algebra .*(.) of differential forms. Useful consequences of this point of view will be treated.

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