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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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
September 2024
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| In: |
Advances in applied mathematics
Year: 2024, Volume: 160, Pages: 1-37 |
| DOI: | 10.1016/j.aam.2024.102753 |
| Online Access: | 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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| Author Notes: | Markus Banagl, Tim Mäder, Filip Sadlo |
| Summary: | 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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| Item Description: | Online verfügbar 12 August 2024 Gesehen am 17.02.2025 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.aam.2024.102753 |