Stratified simple homotopy type

• Verfasst von: Banagl, Markus [VerfasserIn]
• Verfasst von: Mäder, Tim [VerfasserIn]
• Verfasst von: Sadlo, Filip [VerfasserIn]
• Titel: Stratified simple homotopy type
• Titelzusatz: theory and computation
• Verf.angabe: Markus Banagl, Tim Mäder, Filip Sadlo
• E-Jahr: 2024
• Jahr: September 2024
• Umfang: 37 S.
• Illustrationen: Diagramme
• Fussnoten: Online verfügbar 12 August 2024 ; Gesehen am 17.02.2025
• Titel Quelle: Enthalten in: Advances in applied mathematics
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1980
• Jahr Quelle: 2024
• Band/Heft Quelle: 160(2024) vom: Sept., Artikel-ID 102753, Seite 1-37
• DOI: doi:10.1016/j.aam.2024.102753
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Computational topology
• Sach-SW: Simple homotopy theory
• Sach-SW: Stratified spaces
• K10plus-PPN: 1917389515

Abstract

Generalizing the idea of elementary simplicial collapses and expansions in classical simple homotopy theory to a stratified setting, we find local combinatorial transformations on stratified simplicial complexes that leave the global stratified homotopy type invariant. In particular, we obtain the notions of stratified formal deformations generalizing J. H. C. Whitehead's formal deformations. We implement the algorithmic execution of such transformations and the computation of intersection homology to illustrate the behavior of stratified simple homotopy equivalences on Vietoris-Rips type complexes associated to point sets sampled near given, possibly singular, spaces.