Properties and Stability of Persistence Matching Diagrams
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914956665946112 |
|---|---|
| author | Torras-Casas, Alvaro Gonzalez-Diaz, Rocio |
| author_facet | Torras-Casas, Alvaro Gonzalez-Diaz, Rocio |
| contents | We introduce persistence matching diagrams induced by set mappings of metric spaces, based on 0-persistent homology of Vietoris-Rips filtrations. Also, we present a geometric definition of the persistence matching diagram that is more intuitive than the algebraic one. In addition, we show that such matching diagrams encapsulate the information of persistence morphism images, kernels and cokernels induced by embeddings. The main result is a stability theorem for persistence matching diagrams induced by embeddings. At the end, we adapt our stability result for set injections (not embeddings) of finite metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14954 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties and Stability of Persistence Matching Diagrams Torras-Casas, Alvaro Gonzalez-Diaz, Rocio Algebraic Topology We introduce persistence matching diagrams induced by set mappings of metric spaces, based on 0-persistent homology of Vietoris-Rips filtrations. Also, we present a geometric definition of the persistence matching diagram that is more intuitive than the algebraic one. In addition, we show that such matching diagrams encapsulate the information of persistence morphism images, kernels and cokernels induced by embeddings. The main result is a stability theorem for persistence matching diagrams induced by embeddings. At the end, we adapt our stability result for set injections (not embeddings) of finite metric spaces. |
| title | Properties and Stability of Persistence Matching Diagrams |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2409.14954 |