cohomology group

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cohomology group

[′kō·hə′mäl·ə·jē ‚grüp]
(mathematics)
One of a series of Abelian groups Hn (K) that are used in the study of a simplicial complex K and are closely related to homology groups, being associated with cocycles and coboundaries in the same manner as homology groups are associated with cycles and boundaries.
References in periodicals archive ?
2]-level and so at least additively the mod p cohomology is isomorphic to the cotorsion product of the mod p cohomology of G except for the case p = 3, G = [E.
Small) quantum cohomology is a deformation of classical cohomology by the quantum parameter q, and the Schubert basis elements [[sigma].
Finally we observe that, from the continuity of the Cech cohomology functor, we can say that any [R.
Let us mention that if [OMEGA] is a graded differential algebra, then Ker d is the graded unital subalgebra of [OMEGA], whereas Im d is the graded two-sided ideal of Ker d, so the cohomology H([OMEGA]) is the unital associative graded algebra.
Forni, Homology and cohomology with compact supports for q-convex spaces, Ann.
His sophisticated mathematical investigation evaluated ways to associate algebraic structures to topological spaces and proved that loop homology and Hochschild cohomology coincide for an important class of spaces.
De Rham cohomology is a tool belonging to algebraic and differential topology.
There are cohomology relations c(E)c(E) = 1 and [c.
Vaintrob proved that loop homology and Hochschild cohomology coincide for an important class of spaces.
Their cohomology carries actions both of a linear algebraic group (such as gln) and a galois group associated with the number field one is studying.
In particular, they avoid the use of algebraic geometry and results on the cohomology of line bundles over the flag variety that are the standard approach to the theory.
Basic forms are preserved by the exterior derivative and are used to define basic de-Rham cohomology groups [H*.