Titlebook: An Introduction to Manifolds; Loring W. Tu Textbook 2008Latest edition Springer-Verlag New York 2008 Algebraic topology.De Rham cohomology

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,Die ideale moderne Universit?t,Intuitively, a manifold is a generalization of curves and surfaces to arbitrary dimension. While there are many different kinds of manifolds—topological manifolds, .-manifolds, analytic manifolds, and complex manifolds, in this book we are concerned mainly with smooth manifolds.

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,Die ideale moderne Universit?t,Using coordinate charts we can transfer the notion of differentiability from R. to a smooth manifold ..

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Die Universit?ts-Hautklinik MünsterIn this chapter we analyze the local structure of a smooth map on the basis of its rank. Recall that the rank of a smooth map . : . → . at a point . ∈ . is the rank of its differential at .. Two cases are of special interest: when the map . has maximal rank at a point or constant rank in a neighborhood. Let . = dim . and . = dim..

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Anlagebedingte HauterkrankungenCertain manifolds such as the circle have in addition to their . structure also a group structure; moreover, the group operations are .∞. Manifolds such as these are called Lie groups. This chapter is a compendium of a few important examples of Lie groups, the ..

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Alternating k-Linear FunctionsThis chapter is purely algebraic. Its purpose is to develop the properties of alternating .-linear functions on a vector space for later application to the tangent space at a point of a manifold.

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