Morse-based fibering of the persistence rank invariant

DOI10.1007/978-3-030-95519-9_2OpenAlexW3109879278MaRDI QIDQ2080086

Asilata Bapat, Barbara I. Mahler, Celia Hacker, Robyn Brooks, Landi, Claudia

Publication date: 7 October 2022

Full work available at URL: https://arxiv.org/abs/2011.14967

zbMATH Keywords

topological data analysisdiscrete Morse theoryrank invariantmulti-parameter persistent homology

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Discrete Morse theory and related ideas in manifold topology (57Q70) Computational methods for problems pertaining to algebraic topology (55-08)

Uses Software

• GitHub
• RIVET

Cites Work

• Hausdorff stability of persistence spaces
• Reducing complexes in multidimensional persistent homology theory
• Stability of persistence diagrams
• The theory of multidimensional persistence
• A user's guide to discrete Morse theory
• The rank invariant stability via interleavings
• Acyclic partial matchings for multidimensional persistence: algorithm and combinatorial interpretation
• Computing persistent homology
• Generalized persistence algorithm for decomposing multiparameter persistence modules
• Computing multiparameter persistent homology through a discrete Morse-based approach
• The Coherent Matching Distance in 2D Persistent Homology
• Betti numbers in multidimensional persistent homology are stable functions
• Topology and data
• Computing Multidimensional Persistence
• Exact computation of the matching distance on 2-parameter persistence modules
• Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology

This page was built for publication: Morse-based fibering of the persistence rank invariant