Stratified formal deformations and intersection homology of data point clouds
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 part...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
25 May 2020
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| In: |
Arxiv
Year: 2020, Pages: 1-22 |
| DOI: | 10.48550/arXiv.2005.11985 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2005.11985 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2005.11985 
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| Author Notes: | Markus Banagl, Tim Mäder, and Filip Sadlo |
| Summary: | 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. |
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| Item Description: | Gesehen am 06.10.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2005.11985 |