Titlebook: Introduction to Smooth Manifolds; John M. Lee Textbook 2012Latest edition Springer Science+Business Media New York 2012 Frobenius theorem.

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John M. LeeNew edition extensively revised and clarified, and topics have been substantially rearranged.Introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, mu

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978-1-4899-9475-2Springer Science+Business Media New York 2012

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Introduction to Smooth Manifolds978-1-4419-9982-5Series ISSN 0072-5285 Series E-ISSN 2197-5612

镇痛剂

Smooth Maps,t under diffeomorphisms. At the end of the chapter, we introduce a powerful tool for blending together locally defined smooth objects, called .. They are used throughout smooth manifold theory for building global smooth objects out of local ones.

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Tangent Vectors, called the . of the map, and a smooth curve determines a tangent vector at each point, called its .. In the final two sections we discuss and compare several other approaches to defining tangent spaces, and give a brief overview of the terminology of ., which puts the tangent space and differentials in a larger context.

upstart

Submersions, Immersions, and Embeddings,s this discussion is the ., a corollary of the inverse function theorem, which we prove in the first section of the chapter. Then we delve more deeply into smooth embeddings and smooth submersions, and apply the theory to a particularly useful class of smooth submersions, the ..

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,Sard’s Theorem,ontinuous map between smooth manifolds is homotopic to a smooth map. The third result is the ., which says, among other things, that embedded submanifolds can always be deformed slightly so that they intersect “nicely” in a certain sense that we will make precise.

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Lie Groups,are also smooth submanifolds), which lead to a number of new examples of Lie groups. After explaining these basic ideas, we introduce actions of Lie groups on manifolds, which are the primary . of Lie groups. At the end of the chapter, we briefly touch on group representations.