Alvaro Torras-Casas, Rocio Gonzalez-Diaz
Published 2024-09-23Version 1
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.
Nested homotopy models of finite metric spaces and their spectral homology
A Primer on Persistent Homology of Finite Metric Spaces
Properties of Bott manifolds and cohomological rigidity
![QR code for arXiv:2409.14954 [math.AT]](http://oss.arxitics.com/images/favicon.svg)