In mathematics, intersection cohomology is a theory from algebraic topology, initially developed by Goresky and MacPherson, to apply to spaces with singularities.

The cohomology groups of a topological manifold have an interesting symmetry called Poincaré duality. In particular,

,

where n is the dimension of a closed, orientable manifold. Unfortunately, many interesting spaces have singularities; that is, places where the space does not look like Rⁿ. Intersection cohomology is a modified definition of cohomology which recovers the property of Poincaré duality for a much larger category of spaces, Witt spaces ; this includes all algebraic varieties.