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Understanding Intersection Cohomology: A Definitive Guide for Advanced Mathematics
"Intersection cohomology is a powerful generalized cohomology theory for singular algebraic and analytic varieties, developed by Mark Goresky and Robert MacPherson in the late 1970s and early 1980s. It extends classical Poincaré duality to spaces with singularities, providing a foundational tool in modern algebraic geometry, topology, and representation theory. Introduction to Intersection Cohomology In the study of manifolds, smooth spaces enjoy powerful topological properties such as Poincaré duality, which establishes a symmetric pairing between the homology and cohomology groups of complementary dimensions. However, many spaces naturally a..."
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