The singular cohomology of a topological space 
with coefficients in an Abelian
group 
is the cohomology of the cochain
complex obtained by applying the hom functor 
to the singular chain
complex of 
.
Its 
th
cohomology group is
 |
where the coboundary 
is induced by the boundary
operators of the singular chain complex. The
cup product makes these groups into a graded
ring. Singular cohomology defines a contravariant
functor and is distinct from singular homology.
