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  2. Topological manifold - Wikipedia

    en.wikipedia.org/wiki/Topological_manifold

    For example, the E8 manifold is a topological manifold which ... it is at least as hard as the word problem in ... A topological manifold with boundary is a ...

  3. Manifold - Wikipedia

    en.wikipedia.org/wiki/Manifold

    After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line. Considering, for instance, the top part of the unit circle, x 2 + y 2 = 1, where the y-coordinate is positive (indicated by the yellow arc in Figure 1).

  4. 4-manifold - Wikipedia

    en.wikipedia.org/wiki/4-manifold

    The homotopy type of a simply connected compact 4-manifold only depends on the intersection form on the middle dimensional homology. A famous theorem of Michael Freedman () implies that the homeomorphism type of the manifold only depends on this intersection form, and on a / invariant called the Kirby–Siebenmann invariant, and moreover that every combination of unimodular form and Kirby ...

  5. Classification of manifolds - Wikipedia

    en.wikipedia.org/wiki/Classification_of_manifolds

    A topological manifold that is in the image of is said to "admit a differentiable structure", and the fiber over a given topological manifold is "the different differentiable structures on the given topological manifold". Thus given two categories, the two natural questions are:

  6. List of manifolds - Wikipedia

    en.wikipedia.org/wiki/List_of_manifolds

    This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics . For categorical listings see Category:Manifolds and its subcategories.

  7. Topological rigidity - Wikipedia

    en.wikipedia.org/wiki/Topological_rigidity

    A central problem in topology is determining when two spaces are the same i.e. homeomorphic or diffeomorphic. Constructing a morphism explicitly is almost always impractical. If we put further condition on one or both spaces (manifolds) we can exploit this additional structure in order to show that the desired morphism must exist.

  8. Submersion (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Submersion_(mathematics)

    Submersions are also well-defined for general topological manifolds. [3] A topological manifold submersion is a continuous surjection f : M → N such that for all p in M, for some continuous charts ψ at p and φ at f(p), the map ψ −1 ∘ f ∘ φ is equal to the projection map from R m to R n, where m = dim(M) ≥ n = dim(N).

  9. 5-manifold - Wikipedia

    en.wikipedia.org/wiki/5-manifold

    In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure. Non- simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups . [ 1 ]