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This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see Category: ...
Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. CT scans). Manifolds can be equipped with additional structure.
Pages in category "Manifolds" The following 94 pages are in this category, out of 94 total. This list may not reflect recent changes. ...
The Thom isomorphism brings cobordism of manifolds into the ambit of homotopy theory. 1952: Edwin E. Moise: Moise's theorem established that a 3-dimension compact connected topological manifold is a PL manifold (earlier terminology "combinatorial manifold"), having a unique PL
There are two usual ways to give a classification: explicitly, by an enumeration, or implicitly, in terms of invariants. For instance, for orientable surfaces, the classification of surfaces enumerates them as the connected sum of tori, and an invariant that classifies them is the genus or Euler characteristic.
The objects of Man • p are pairs (,), where is a manifold along with a basepoint , and its morphisms are basepoint-preserving p-times continuously differentiable maps: e.g. : (,) (,), such that () =. [1] The category of pointed manifolds is an example of a comma category - Man • p is exactly ({}), where {} represents an arbitrary singleton ...
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.
Another, more topological example of an intrinsic property of a manifold is the Euler characteristic. For a non-intersecting graph in the Euclidean plane, with V vertices (or corners), E edges and F faces (counting the exterior) Euler showed that V-E+F= 2. Thus 2 is called the Euler characteristic of the plane.