Homology of Conically Smooth Manifolds via Links

Given a "nice" smooth manifold we may affix it with additional mathematical structure to be able to apply further machinery to explicitly compute its (co)homology. Namely, we can affix a well-behaved (poset-)stratification along with the notion of conical smoothness to guarantee we can ”unzip” our space into disjoint copies of Euclidean space while remembering how these pieces interconnect using iterated blowups to construct an associated complex for the given manifold. Then, once we have successfully constructed the appropriate complex of the manifold, we may use spectral sequence methods to compute its homology. In this talk, I will provide some background to solidify these concepts as well as provide a sketch of the proof of the related proposition.