Singular cohomology
= Singular cohomology
{title2=$H^n(X;A)$}
For a <topological space> $X$ and <abelian group> $A$, singular cohomology is the <cohomology> of the <cochain complex> $C^n(X;A)=\operatorname{Hom}(C_n(X;\mathbb Z),A)$, where $C_n$ is the <singular chain group>. Its differential is dual to the singular boundary. This theory has <relative cohomology>, <long exact sequences> and the <Excision theorem>. On spaces that are not locally contractible it can differ from <Čech cohomology>.