Chain (algebraic topology)

In algebraic topology, a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k-chains are combinations of k-simplices (respectively, k-cubes), but not necessarily connected. Chains are used in homology; the elements of a homology group are equivalence classes of chains.

This article is about algebraic topology. For the term chain in order theory, see chain (order theory).
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