2022/11/11 by David Chataur, Chataur, David, Martintxo Saralegi-Aranguren +3 · 1 citation
Mathematics · #14F43 #55M10 #55N33 #55Q70 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2211.06096
openalex publication_date 2022/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to a couple (X,p) of a filtered space and a perversity. We first establish some basic properties for the intersection fundamental groups, as a Van Kampen theorem. For general intersection homotopy groups on Siebenmann CS sets, we prove a Hurewicz theorem between them and the Goresky and MacPherson intersection homology. If the CS set and its intrinsic stratification have the same regular part, we establish the topological invariance of the p-intersection homotopy groups. Several examples justify the hypotheses made in the statements. Finally, intersection homotopy groups also coincide with the homotopy groups of the topological space itself, for the top perversity on a connected, normal Thom-Mather space.