Intersection cohomology, simplicial blow-up and rational homotopy - Chataur, David, 1974-; Saralegi-Aranguren, Martintxo, 1960-; Tanré, Daniel (Memoirs of the American Mathematical Society, 2018)
Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C.P. Rourke and B.J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above whe.