Stratified formal deformations and intersection homology of data point clouds

• Verfasst von: Banagl, Markus [VerfasserIn]
• Verfasst von: Mäder, Tim [VerfasserIn]
• Verfasst von: Sadlo, Filip [VerfasserIn]
• Titel: Stratified formal deformations and intersection homology of data point clouds
• Verf.angabe: Markus Banagl, Tim Mäder, and Filip Sadlo
• E-Jahr: 2020
• Jahr: 25 May 2020
• Umfang: 22 S.
• Fussnoten: Gesehen am 06.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2020
• Band/Heft Quelle: (2020), Artikel-ID 2005.11985, Seite 1-22
• DOI: doi:10.48550/arXiv.2005.11985
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 55N33, 68
• Sach-SW: Computer Science - Computational Geometry
• Sach-SW: Mathematics - Algebraic Topology
• K10plus-PPN: 1818129094

Abstract

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.