2020/05/25 by Markus Banagl, Banagl, Markus, Tim Mäder +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #55N33 #68 #Algebraic Topology (math.AT) #Cell Image Analysis Techniques #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #cs.CG #math.AT #msc:55N33 #msc:68
paper · pdf · doi:10.48550/arxiv.2005.11985
11 figures
arxiv created 2020/05/25 · openalex publication_date 2020/05/25 · arxiv updated 2020/05/26 · openalex created_date 2020/05/29 · openalex updated_date 2026/07/28
Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes under which intersection homology remains invariant. In particular, we obtain the notions of stratified formal deformations and stratified spines of a complex, leading to reductions of complexes prior to computation of intersection homology. We implemented the algorithmic execution of such transformations, as well as the calculation of intersection homology, and apply these algorithms to investigate the intersection homology of stratified spines in Vietoris-Rips type complexes associated to point sets sampled near given, possibly singular, spaces.