Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability
Algebraic Topology
2021-07-07 v5
Abstract
Persistent homology studies the birth and death of cycles in a parameterized family of spaces. In this paper, we study the birth and death of cycles in a multifiltration of a chain complex with the goal of producing a persistence diagram that satisfies bottleneck stability.
Keywords
Cite
@article{arxiv.1905.13220,
title = {Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability},
author = {Alex McCleary and Amit Patel},
journal= {arXiv preprint arXiv:1905.13220},
year = {2021}
}
Comments
The claim that Dgm(S^n) is finite is not true. Our second paper "Edit Distance and Persistence Diagrams over Lattice" on multiparameter persistent homology also using the Mobius inversion formula is more to our liking