chain complex

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chain complex

[′chān ‚käm‚pleks]
(mathematics)
A sequence {Cn }, -∞ <>n < ∞,="" of="" abelian="" groups="" together="" with="" a="" sequence="" of="" boundary="" homomorphisms="">dn : CnCn-1such that dn-1° dn = 0 for each n.
References in periodicals archive ?
Chataur, Saralegi-Aranguren, and Tanreuse a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field is isomorphic to the intersection cohomology of a pseudo-manifold introduced by M.
In a 2-D or 3-D simplicial mesh, if there are [N.sub.1] edges in total, 1- cochain E can be defined as:
If an N-graded ring also is a cochain complex, we come to the following notion [5,17].
The homology of the cochain complex ([C.sup.*] (G,A), [[partial derivative].sup.*]) is called the cohomology of G with coefficients in A
Wilson, Cochain algebra on manifolds and convergence under refinement, Topology Appl.
(57.) Leroyer AS, Ebrahimian TG, Cochain C, Recalde A, Blanc-Brude O, Mees B, et al.
In Section 2 and Section 3 we give a short overview of N-structures, such as N-differential module, cochain N-complex, generalized cohomologies of an N-complex, and graded q-differential algebra.
Likewise the map U makes them into cochain complexes, i.e., [U.sup.2] = 0.
is called a weak bounding cochain, which can be used to define the deformed Floer cohomology.
An easy but rather lengthy calculation proves that the map d is nilpotent and that the composition (3.2) is a morphism of cochain complexes.
[EM] The cochain ([alpha], [beta], [gamma]) [right arrow] [kappa]([alpha], [beta], [gamma]) is a cocycle.
Let us define a map k: D(A) [right arrow] D(A') of cochain complexes by k{[sigma]) = 0 if [x.sub.0] [member of] [sigma] and k([sigma]) = a if [x.sub.0] [??] [sigma].