| Autor: |
Adamaszek, Michal, Adams, Henry, Gasparovic, Ellen, Gommel, Maria, Purvine, Emilie, Sazdanovic, Radmila, Wang, Bei, Wang, Yusu, Ziegelmeier, Lori |
| Rok vydání: |
2017 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s41468-020-00054-y |
| Popis: |
We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips complexes. We also provide generalizations for when two metric spaces are glued together along a common isometric subset. As our main example, we deduce the homotopy type of the Vietoris-Rips complex of two metric graphs glued together along a sufficiently short path (compared to lengths of certain loops in the input graphs). As a result, we can describe the persistent homology, in all homological dimensions, of the Vietoris-Rips complexes of a wide class of metric graphs. |
| Databáze: |
arXiv |
| Externí odkaz: |
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