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Generally, a chain is an element of a chain complex. Specifically for the complex computing the singular homology of a topological space, a singular chain is a formal linear combination of simplices in that space. In de Rham cohomology, a de Rham chain? is a formal linear combination of parametrized submanifold?s with boundary.
In order homology theory , / the term has another meaning: a totally homological ordered algebra , asubsetchain is an element of a givenposetchain complex (or proset). See Zorn's Lemma for an application of this concept; see also antichain.
Specifically for the complex computing the singular homology of a topological space, a singular chain is a formal linear combination of simplices in that space.
In de Rham cohomology, a de Rham chain? is a formal linear combination of parametrized submanifolds? with boundary.
In order theory, a chain is a totally ordered subset of a given poset (or proset). See also antichain
For applications of this concept see for instance
| (chain-)homology | (cochain-)cohomology | ||
|---|---|---|---|
| chain | cochain | ||
| cycle | cocycle | ||
| boundary | coboundary |
Last revised on December 4, 2022 at 07:49:46. See the history of this page for a list of all contributions to it.