Homology with coefficients

Summary

Homology with coefficients in an abelian group $G$ is singular homology computed with chains whose coefficients lie in $G$ instead of $\Z$. Coefficients in a field such as $\Q$ or $\Z/p$ give vector spaces, which are easier to handle, and coefficients in $\Z/2$ remove all sign questions. The universal coefficient theorem recovers the homology with any coefficients from the integral homology.