nLab
chain

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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.

H n=Z n/B n(chain-)homology(cochain-)cohomologyH n=Z n/B n
C nchaincochainC n
Z n⊂C ncyclecocycleZ n⊂C n
B n⊂C nboundarycoboundaryB n⊂C n

Created on August 27, 2012 00:39:28 by Urs Schreiber (89.204.139.66)
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