Morse inequalities for the Koszul complex of multi-persistence

DOI10.1016/j.jpaa.2023.107319OpenAlexW3196000381MaRDI QIDQ2690451

Andrea Guidolin, Landi, Claudia

Publication date: 17 March 2023

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.11427

zbMATH Keywords

Euler characteristicpersistence modulemultigraded Betti numbersMayer-Vietoris spectral sequencehomological Morse numbers

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Syzygies, resolutions, complexes and commutative rings (13D02) Chain complexes in algebraic topology (55U15) Discrete Morse theory and related ideas in manifold topology (57Q70)

Uses Software

• RIVET

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Morse theory for filtrations and efficient computation of persistent homology
• Discrete Morse theoretic algorithms for computing homology of complexes and maps
• Reducing complexes in multidimensional persistent homology theory
• An introduction to homological algebra
• The theory of multidimensional persistence
• Morse theory for cell complexes
• Computing persistent homology
• An approximate nerve theorem
• Topological persistence and simplification
• Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology
• A refinement of multi-dimensional persistence
• Discrete Morse theory for free chain complexes
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• Topology and data
• Computing Multidimensional Persistence
• The Homology Products in K(II, n)
• Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology