# Intersection cohomology

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,

[itex]H^k(X) \equiv H_{n-k}(X)[itex],

where [itex]n[itex] is the dimension of a closed, orientable manifold. Unfortunately, many interesting spaces have singularities; that is, places where the space does not look like [itex]R^n[itex]. 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.Template:Geometry-stub

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