Let C denote a chain complex, a portion of which is shown below:


Let H_n(C)=kerpartial_n/Impartial_(n+1) denotes the nth homology group. Then two homology cycles u,v in kerpartial_n are said to be homologous, if their difference is a boundary, i.e., if u-v in Impartial_(n+1).

This entry contributed by Rasmus Hedegaard

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Hedegaard, Rasmus. "Homologous." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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