nLab cycle

• in group theory: cycle of a permutation

• in homological algebra: cycle in a chain complex

  in algebraic topology a representative for a class in a homology theory

$H_n = Z_n/B_n$	(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	$B^n \subset C^n$

e.g.

• Baum-Douglas geometric cycle

category: disambiguation