Cellular chain group
= Cellular chain group
{title2=$C_q^{\mathrm{cell}}(X)=H_q(X^q,X^{q-1};\mathbb Z)$}
For a <CW complex>, the qth <cellular chain group> is the relative <homology group> of successive skeleta, a <free abelian group> with one generator for each q-cell. The attaching maps determine the <cellular boundary>, and the resulting <cellular chain complex> computes <singular homology>.