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DOI: 10.4230/LIPIcs.SoCG.2018.3
URN: urn:nbn:de:0030-drops-87162
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8716/
Adamaszek, Michal ; Adams, Henry ; Gasparovic, Ellen ; Gommel, Maria ; Purvine, Emilie ; Sazdanovic, Radmila ; Wang, Bei ; Wang, Yusu ; Ziegelmeier, Lori
Vietoris-Rips and Cech Complexes of Metric Gluings
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Abstract
We study Vietoris-Rips and Cech complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips (resp. Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp. Cech) complexes. We also provide generalizations for certain metric gluings, i.e. 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. 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.
BibTeX - Entry
@InProceedings{adamaszek_et_al:LIPIcs:2018:8716,
author = {Michal Adamaszek and Henry Adams and Ellen Gasparovic and Maria Gommel and Emilie Purvine and Radmila Sazdanovic and Bei Wang and Yusu Wang and Lori Ziegelmeier},
title = {{Vietoris-Rips and Cech Complexes of Metric Gluings}},
booktitle = {34th International Symposium on Computational Geometry (SoCG 2018)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-066-8},
ISSN = {1868-8969},
year = {2018},
volume = {99},
editor = {Bettina Speckmann and Csaba D. T{\'o}th},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8716},
URN = {urn:nbn:de:0030-drops-87162},
doi = {10.4230/LIPIcs.SoCG.2018.3},
annote = {Keywords: Vietoris-Rips and Cech complexes, metric space gluings and wedge sums, metric graphs, persistent homology}
}
| Keywords: | Vietoris-Rips and Cech complexes, metric space gluings and wedge sums, metric graphs, persistent homology | |
| Seminar: | 34th International Symposium on Computational Geometry (SoCG 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 08.06.2018 |
