Intersection cohomology

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

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

:H^k(X) equiv H_{n-k}(X),

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 R^n. 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.