• mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important...
    17 KB (2,041 words) - 19:00, 28 June 2024
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    manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...
    68 KB (9,509 words) - 09:52, 30 June 2024
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    terms, a differentiable manifold is a topological manifold with a globally defined differential structure. Any topological manifold can be given a differential...
    67 KB (9,509 words) - 20:55, 28 June 2024
  • contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds which admit no smooth structure...
    15 KB (1,940 words) - 01:03, 26 October 2023
  • In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure...
    6 KB (749 words) - 03:56, 30 March 2024
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    Topology (redirect from Topological)
    topological field theory. The topological classification of Calabi–Yau manifolds has important implications in string theory, as different manifolds can...
    35 KB (4,041 words) - 07:16, 10 June 2024
  • differential manifold, which is a topological manifold with some additional structure that allows for differential calculus on the manifold. If M is already...
    10 KB (1,342 words) - 21:50, 23 April 2024
  • Smooth structure (category Structures on manifolds)
    equivalence relation on the set of smooth atlases. A smooth manifold is a topological manifold M {\displaystyle M} together with a smooth structure on M...
    4 KB (520 words) - 20:22, 27 November 2023
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    is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent...
    25 KB (3,515 words) - 23:28, 21 May 2024
  • manifolds is much more subtle than that of differentiable manifolds. For example, while in dimensions other than four, a given topological manifold has...
    10 KB (1,306 words) - 04:22, 4 June 2024