 Intersection homology

Intersection homology is the homology of a chain complex in which chains and their boundaries satisfy codimension-dependent perversity restrictions at singular strata. Unless specified otherwise coefficients here are $\mathbb{Q}$. Ordinary homology is recovered on manifolds.

Intersection homology is a mathematical concept in algebraic topology that generalizes the notion of homology for singular spaces, particularly for spaces that may have singularities or non-manifold structures. Developed by mathematician Goresky and MacPherson in the 1980s, intersection homology provides tools to study these more complex spaces in a way that is coherent with classical homology theory.