Contents

# Contents

## Idea

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 theory, the term has another meaning: a totally ordered subset of a given poset (or proset). See Zorn's Lemma for an application of this concept; see also antichain.

$H_n = Z_n/B_n$(chain-)homology(cochain-)cohomology$H^n = Z^n/B^n$
$C_n$chaincochain$C^n$
$Z_n \subset C_n$cyclecocycle$Z^n \subset C^n$
$B_n \subset C_n$boundarycoboundary$B^n \subset C^n$

Last revised on September 17, 2018 at 02:29:59. See the history of this page for a list of all contributions to it.