fundamental manifold

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• Fundamental class — For the fundamental class in class field theory see class formation. In mathematics, the fundamental class is a homology class [M] associated to an oriented manifold M, which corresponds to the whole manifold , and pairing with which corresponds… …   Wikipedia

• Fundamental theorem of calculus — The fundamental theorem of calculus specifies the relationship between the two central operations of calculus, differentiation and integration.The first part of the theorem, sometimes called the first fundamental theorem of calculus, shows that… …   Wikipedia

• Fundamental polygon — In mathematics, each closed surface in the sense of geometric topology can be constructed from an even sided oriented polygon, called a fundamental polygon, by pairwise identification of its edges. Fundamental parallelogram defined by a pair of… …   Wikipedia

• Fundamental theorem of Riemannian geometry — In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo Riemannian manifold) there is a unique torsion free metric connection, called the Levi Civita connection of the given metric …   Wikipedia

• Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

• Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

• Fundamental pair of periods — In mathematics, a fundamental pair of periods is an ordered pair of complex numbers that define a lattice in the complex plane. This type of lattice is the underlying object with which elliptic functions and modular forms are defined. Although… …   Wikipedia

• Fundamental vector field — In mathematics, a fundamental vector field is a vector field on a manifold which is induced by a group action.DefinitionLet M be a manifold and G a Lie group with left action l on M , l : G imes M o M. Now define:zeta : mathfrak{g} o… …   Wikipedia

• Spherical 3-manifold — In mathematics, a spherical 3 manifold M is a 3 manifold of the form M = S3 / Γ where Γ is a finite subgroup of SO(4) acting freely by rotations on the 3 sphere S3. All such manifolds are prime, orientable, and closed. Spherical 3 manifolds are… …   Wikipedia

• Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

• 4-manifold — In mathematics, 4 manifold is a 4 dimensional topological manifold. A smooth 4 manifold is a 4 manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different.… …   Wikipedia