Goresky-MacPherson Formula

The Goresky-MacPherson formula provides a way to compute the topology (specifically, the cohomology groups) of the complement of a complicated shape (like a union of subspaces) within a larger space. It relates the cohomology of the space minus these subspaces to the cohomology of their intersections, organized through combinatorial data called a stratification. In essence, it breaks down complex geometric problems into manageable pieces, allowing mathematicians to understand how the structure of the parts and their overlaps determine the overall shape's topological features.