Chain Homotopy
Chain homotopies give an important equivalence relation between chain maps. Chain homotopic chain maps induce the same maps on homology groups. A particular case is that homotopic maps between two spaces X and Y induce the same maps from homology of X to homology of Y. Chain homotopies have a geometric interpretation; it is described, for example, in the book of Bott and Tu. See Homotopy category of chain complexes for further information.
Read more about this topic: Chain Complex
Famous quotes containing the word chain:
“By this unprincipled facility of changing the state as often, and as much, and in as many ways as there are floating fancies or fashions, the whole chain and continuity of the commonwealth would be broken. No one generation could link with the other. Men would become little better than the flies of a summer.”
—Edmund Burke (1729–1797)