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Introduction to Topological Manifolds, Springer-Verlag, Graduate Texts in Mathematics 2000, 2nd edition 2011 [5] Lee, John M. (2012). Introduction to Smooth Manifolds. Graduate Texts in Mathematics. Vol. 218 (Second ed.). New York London: Springer-Verlag. ISBN 978-1-4419-9981-8. OCLC 808682771.
Download as PDF; Printable version; In other projects Wikidata item; ... {Lee Introduction to Smooth Manifolds|edition=2}} and then add a citation by using the markup
Michele Audin, Torus actions on symplectic manifolds, Birkhauser, 2004 John Lee, Introduction to smooth manifolds , chapter 9, ISBN 978-1-4419-9981-8 Frank Warner, Foundations of differentiable manifolds and Lie groups , chapter 3, ISBN 978-0-387-90894-6
The occasion of the proof by Hassler Whitney of the embedding theorem for smooth manifolds is said (rather surprisingly) to have been the first complete exposition of the manifold concept precisely because it brought together and unified the differing concepts of manifolds at the time: no longer was there any confusion as to whether abstract ...
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Depending on the precise definition and the category of manifolds (smooth, PL, or topological), there are various versions of structure sets. Since, by the s-cobordism theorem, certain bordisms between manifolds are isomorphic (in the respective category) to cylinders, the concept of structure set allows a classification even up to diffeomorphism.
Theorem: Every smooth manifold admits a (non-canonical) Riemannian metric. [13] This is a fundamental result. Although much of the basic theory of Riemannian metrics can be developed using only that a smooth manifold is a locally Euclidean topological space, for this result it is necessary to use that smooth manifolds are Hausdorff and paracompact.
Vector field corresponding to a differential form on the punctured plane that is closed but not exact, showing that the de Rham cohomology of this space is non-trivial.. In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form ...