Intersection Cohomology. Simplicial Blow-up and Rational Homotopy

David Chataur (1) , Daniel Tanré (2) , Martintxo Saralegi-Aranguren (3)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 LML - Laboratoire de Mathématiques de Lens

In this text, we extend Sullivan's presentation of rational homotopy type to Goresky and MacPherson's intersection cohomology. We choose the context of face sets, also called simplicial sets without degeneracies, in the sense of Rourke and Sanderson. We define filtered face sets, perverse local systems over them and intersection cohomology with coe

Keywords: Intersection homology. Intersection cohomology. Thom-Whitney cohomology. Balanced perverse complex. Sullivan minimal model. Blow-up. Formality. Perverse local systems. Filtered spaces. Stratified spaces. CS sets. Pseudomanifolds. Topological invariance. Isolated singularities. Thom spaces. Nodal hypersurfaces. Morgan’s model for the complement of a divisor

Domains: Mathematics [math]; Algebraic Topology [math.AT]; Mathematics [math]; Geometric Topology [math.GT]

David Chataur, Daniel Tanré, Martintxo Saralegi-Aranguren. Intersection Cohomology. Simplicial Blow-up and Rational Homotopy. Memoirs of the American Mathematical Society, 2018, 254 (1214), viii+108 pp. ⟨hal-00727650⟩