Properties and Stability of Persistence Matching Diagrams
Algebraic Topology
2024-09-26 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2409.14954,
title = {Properties and Stability of Persistence Matching Diagrams},
author = {Alvaro Torras-Casas and Rocio Gonzalez-Diaz},
journal= {arXiv preprint arXiv:2409.14954},
year = {2024}
}