2022/12/07 by Sebastian Cea, Cea, Sebastian
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2212.03379
openalex publication_date 2022/12/07 · openalex created_date 2022/12/21 · openalex updated_date 2026/07/28
Intersection cohomology is a way to enhance classical cohomology, allowing us to use a famous result called Poincaré duality on a large class of spaces known as stratified pseudomanifolds. There is a theoretically powerful way to arrive at intersection cohomology by classifying sheaves that satisfy what are called Deligne axioms. We stablish an abstract manifestation of the Deligne axioms, to then apply it on a simplicial complex environment, for a category of simplicial sheaves inspired on the works of D. Chataur, D. Tanré and M. Saralegi-Araguren. For a stablished topology on a triangulation of a stratified pseudomanifold, we find a family of sheaves satisfying the simplicial Deligne axioms, giving us a way to construct intersection cohomology from simplicial sheaves.