Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability

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.

arXiv commentThe 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

References in corpus (5)

• The Theory of the Interleaving Distance on Multidimensional Persistence Modules
• Interactive Visualization of 2-D Persistence Modules
• Generalized Persistence Diagrams
• Bottleneck Stability for Generalized Persistence Diagrams
• Higher interpolation and extension for persistence modules

Cited by in corpus (3)

• Graded persistence diagrams and persistence landscapes
• Elder-Rule-Staircodes for Augmented Metric Spaces
• Local Equivalence of Metrics for Multiparameter Persistence Modules