Chain Homotopy
Suppose alpha:C_*->D_* and beta:C_*->D_* are two chain homomorphisms. Then a chain homotopy is given by a sequence of maps
| delta_p:C_p->D_(p-1) |
such that
| partial_D degreesdelta+delta degreespartial_C=alpha-beta, |
where partial denotes the boundary operator.
See also
Chain Complex, Chain Equivalence, Chain Homomorphism, Homotopy, Snake LemmaThis entry contributed by Todd Rowland
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Cite this as:
Rowland, Todd. "Chain Homotopy." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ChainHomotopy.html