Definition of Cochain. Meaning of Cochain. Synonyms of Cochain

- kernels. A cochain complex is similar to a chain complex, except that its homomorphisms are in the opposite direction. The homology of a cochain complex...
- {F}})} is an abelian group by pointwise addition. The cochain groups can be made into a cochain complex ( C ∙ ( U , F ) , δ ) {\displaystyle (C^{\bullet...
- In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential...
- whole interval which makes the difference quotient a 1 {\displaystyle 1} -cochain. The most common notation for the difference quotient is: Δ f Δ x ( x +...
- usually one ****ociated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of ****igning richer algebraic...
- homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification of the Jones polynomial...
- space and G is an R module where R is a ring with unity, then there is a cochain complex C whose p-th term C p {\displaystyle C^{p}} is the set of all functions...
- This is an abelian group; its elements are called the (inhomogeneous) n-cochains. The coboundary homomorphisms are defined by { d n + 1 : C n ( G , M )...
- πn(F)-valued simplicial cochain of degree n + 1 on B, i.e. an element of Cn + 1(B; πn(F)). This cochain is called the obstruction cochain because it being the...
- quasi-isomorphism or quism is a morphism A → B of chain complexes (respectively, cochain complexes) such that the induced morphisms H n ( A ∙ ) → H n ( B ∙ )  ...