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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: ...
Pages in category "Manifolds" The following 94 pages are in this category, out of 94 total. This list may not reflect recent changes. ...
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for ...
Manifolds in contemporary mathematics come in a number of types. These include: smooth manifolds, which are basic in calculus in several variables, mathematical analysis and differential geometry; piecewise-linear manifolds; topological manifolds. There are also related classes, such as homology manifolds and orbifolds, that resemble manifolds.
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 ...
See also multivariable calculus, list of multivariable calculus topics. Manifold. Differentiable manifold; Smooth manifold; Banach manifold; Fréchet manifold; Tensor analysis. Tangent vector
The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups.
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.