in group theory: cycle of a permutation
in homological algebra: cycle in a chain complex
more generally: in a homology theory a representative for a class
$H_n = Z_n/B_n$ | (chain-)homology | (cochain-)cohomology | $H^n = Z^n/B^n$ |
---|---|---|---|
$C_n$ | chain | cochain | $C^n$ |
$Z_n \subset C_n$ | cycle | cocycle | $Z^n \subset C^n$ |
$B_n \subset C_n$ | boundary | coboundary | $B^n \subset C^n$ |
Last revised on June 9, 2013 at 00:35:56. See the history of this page for a list of all contributions to it.