TOPICS
Search

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 Lemma

This entry contributed by Todd Rowland

Explore with Wolfram|Alpha

Cite this as:

Rowland, Todd. "Chain Homotopy." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ChainHomotopy.html

Subject classifications