Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability

2019/05/30 by McCleary, Alex, Patel, Amit
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.13220

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.

Related

• On persistent homology of random Čech complexes
• Convergence of Persistence Diagrams for Topological Crackle
• Persistent homology of Morse decomposition in Markov chains based on combinatorial multivector fields
• Multiparameter persistence modules in the large scale
• Computing Optimal Persistent Cycles for Levelset Zigzag on Manifold-like Complexes