Intersection cohomology
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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,
- <math>H^k(X) \equiv H_{n-k}(X)<math>,
where <math>n<math> is the dimension of a closed, orientable manifold. Unfortunately, many interesting spaces have singularities; that is, places where the space does not look like <math>R^n<math>. 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