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
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“It is the future that creates his present.
All is an interminable chain of longing.”
—Robert Frost (18741963)
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