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