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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: ...
Category of manifolds; Classification of manifolds; Closed manifold; Collapsing manifold; Collar neighbourhood; Complete manifold; Complex Lie group; Configuration space (mathematics) Conformally flat manifold; Crumpling
Figure 1: The four charts each map part of the circle to an open interval, and together cover the whole circle. After a line, a circle is the simplest example of a topological manifold.
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 ...
Kähler manifold; Dolbeault operator; CR manifold; Stein manifold; Almost complex structure; Hermitian manifold; Newlander–Nirenberg theorem; Generalized complex manifold; Calabi–Yau manifold; Hyperkähler manifold; K3 surface; hypercomplex manifold; Quaternion-Kähler manifold
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 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.
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.
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