Chain cycle
= Chain cycle
{title2=$Z_n(C)=\ker\partial_n$}
= Cycle in a chain complex
{synonym}
= Homological cycle
{synonym}
An element of a <chain group> is a cycle when its <boundary operator> kills it. A cycle need not itself be a <chain boundary>. The <homology group> $H_n(C)$ identifies cycles whose difference is a <chain boundary>.