Computing Connection Matrices via Persistence-Like Reductions

DOI10.1137/23m1562469arXiv2303.02549OpenAlexW4390586483MaRDI QIDQ6144483

Michał Lipiński, Tamal Krishna Dey, Ryan Slechta, Marian Mrozek

Publication date: 29 January 2024

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.02549

zbMATH Keywords

persistencedynamical systemconnection matrixmatrix reductioncombinatorial (multi) vector fieldConley complex

Mathematics Subject Classification ID

General topology of complexes (57Q05) Triangulating manifolds (57Q15) Discrete Morse theory and related ideas in manifold topology (57Q70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Towards a formal tie between combinatorial and classical vector field dynamics
• Homology computation by reduction of chain complexes
• Combinatorial vector fields and dynamical systems
• Morse theory for cell complexes
• Optimal discrete Morse functions for 2-manifolds
• Computational homology
• Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes
• Creating semiflows on simplicial complexes from combinatorial vector fields
• A computational framework for connection matrix theory
• Barcodes of towers and a streaming algorithm for persistent homology
• Efficient Computation of Persistent Homology for Cubical Data
• Index Filtrations and the Homology Index Braid for Partially Ordered Morse Decompositions
• The Connection Matrix Theory for Morse Decompositions
• Dualities in persistent (co)homology
• Topological sorting of large networks
• Lyapunov maps, simplicial complexes and the Stone functor
• Clear and Compress: Computing Persistent Homology in Chunks
• Morse decompositions and connection matrices
• Computational Topology for Data Analysis
• Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems
• Persistent Homology of Morse Decompositions in Combinatorial Dynamics
• Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces