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  2. 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.

  3. Topological manifold - Wikipedia

    en.wikipedia.org/wiki/Topological_manifold

    It is common to place additional requirements on topological manifolds. In particular, many authors define them to be paracompact [3] or second-countable. [2] In the remainder of this article a manifold will mean a topological manifold. An n-manifold will mean a topological manifold such that every point has a neighborhood homeomorphic to R n.

  4. List of topologies - Wikipedia

    en.wikipedia.org/wiki/List_of_topologies

    The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property .

  5. 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).

  6. List of topology topics - Wikipedia

    en.wikipedia.org/wiki/List_of_topology_topics

    The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. This is a list of topology topics. See also: Topology glossary; List of topologies; List of general topology topics; List of geometric topology topics

  7. List of geometric topology topics - Wikipedia

    en.wikipedia.org/wiki/List_of_geometric_topology...

    Examples of knots Unknot; ... Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups; ... List of topology topics;

  8. 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:

  9. 4-manifold - Wikipedia

    en.wikipedia.org/wiki/4-manifold

    In dimension 3 and lower, every topological manifold admits an essentially unique PL structure. In dimension 4 there are many examples with vanishing Kirby–Siebenmann invariant but no PL structure. In any dimension other than 4, a compact topological manifold has only a finite number of essentially distinct PL or smooth structures.