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  2. Topological manifold - Wikipedia

    en.wikipedia.org/wiki/Topological_manifold

    All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold (e.g. differentiable manifolds are topological manifolds equipped with a differential structure). Every manifold has an "underlying" topological manifold, obtained by simply "forgetting" the added structure. [1]

  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. 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.

  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. Surface (topology) - Wikipedia

    en.wikipedia.org/wiki/Surface_(topology)

    An open surface with x-, y-, and z-contours shown.. In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball.

  7. Category:Structures on manifolds - Wikipedia

    en.wikipedia.org/wiki/Category:Structures_on...

    There are three main types of structures important on manifolds. The foundational geometric structures are piecewise linear, mostly studied in geometric topology, and smooth manifold structures on a given topological manifold, which are the concern of differential topology as far as classification goes. Building on a smooth structure, there are:

  8. (G,X)-manifold - Wikipedia

    en.wikipedia.org/wiki/(G,X)-manifold

    In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structure are always manifolds and are called (G, X)-manifolds.

  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 ]