Stratified simple homotopy type: theory and computation
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 n...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
September 2024
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| In: |
Advances in applied mathematics
Year: 2024, Jahrgang: 160, Pages: 1-37 |
| DOI: | 10.1016/j.aam.2024.102753 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.aam.2024.102753 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S019688582400085X 
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| Verfasserangaben: | Markus Banagl, Tim Mäder, Filip Sadlo |
| Zusammenfassung: | 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. |
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| Beschreibung: | Online verfügbar 12 August 2024 Gesehen am 17.02.2025 |
| Beschreibung: | Online Resource |
| DOI: | 10.1016/j.aam.2024.102753 |