Bottleneck Stability for Generalized Persistence Diagrams

Abstract

In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.

arXiv commentWe have made major revisions to this paper. We have streamlined our arguments and cleaned up the appalling number of typos

References in corpus (3)

• The Theory of the Interleaving Distance on Multidimensional Persistence Modules
• Generalized Persistence Diagrams
• Higher interpolation and extension for persistence modules

Cited by in corpus (7)

• Generalized Persistence Diagrams for Persistence Modules over Posets
• Edit Distance and Persistence Diagrams Over Lattices
• Graded persistence diagrams and persistence landscapes
• Capturing Dynamics of Time-Varying Data via Topology
• Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability
• Universal Distances for Extended Persistence
• Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations