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14 relations: Closed and exact differential forms, De Rham cohomology, Differential form, Differential geometry, Exact sequence, Fiber bundle, Gysin homomorphism, Homotopy category of chain complexes, Manifold, Michèle Audin, Orientation of a vector bundle, Sphere bundle, Stokes' theorem, Transgression map.
Closed and exact differential forms
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα.
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De Rham cohomology
In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes.
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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Exact sequence
An exact sequence is a concept in mathematics, especially in group theory, ring and module theory, homological algebra, as well as in differential geometry.
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Fiber bundle
In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.
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Gysin homomorphism
In the field of mathematics known as algebraic topology, the Gysin sequence is a long exact sequence which relates the cohomology classes of the base space, the fiber and the total space of a sphere bundle.
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Homotopy category of chain complexes
In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Michèle Audin
Michèle Audin is a French mathematician, writer, and a former professor.
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Orientation of a vector bundle
In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle π: E →B, an orientation of E means: for each fiber Ex, there is an orientation of the vector space Ex and one demands that each trivialization map (which is a bundle map) is fiberwise orientation-preserving, where Rn is given the standard orientation.
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Sphere bundle
In the mathematical field of topology, a sphere bundle is a fiber bundle in which the fibers are spheres S^n of some dimension n. Similarly, in a disk bundle, the fibers are disks D^n.
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Stokes' theorem
In vector calculus, and more generally differential geometry, Stokes' theorem (also called the generalized Stokes theorem or the Stokes–Cartan theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
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Transgression map
In algebraic topology, a transgression map is a way to transfer cohomology classes.
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