Let \(X\) be a topological space and \(n\geq 0\). Two cycles \(\alpha, \beta \in Z_n(X)\) are homologous if there exists \(\gamma\in C_{n+1}(X)\) with \(\alpha - \beta = \del_{n+1}\gamma\).
Two cycles are homologous if and only if they represent the same class in the singular homology group \(H_n(X)\).
[@Hat02].