A homology cycle of degree 
is an element of the kernel
of the boundary operator 
in a chain complex of modules,
 |
The module of 
-cycles is
 |
Thus 
is a submodule of 
, while 
is the boundary
operator.
Homology Cycle
See also
Cocycle, Homology, Homology BoundaryPortions of this entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Homology Cycle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HomologyCycle.html