The Theory of Multidimensional Persistence

2009/04/23 by Gunnar Carlsson, Afra Zomorodian · 241 citations
Computer Science · Mathematics · #Algorithm #Betti number #Combinatorics #Discrete mathematics #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical analysis #Mathematics #Multiset #Parameterized complexity #Persistent homology #Pure mathematics #Subspace topology #Topological and Geometric Data Analysis #Topology (electrical circuits)

paper · pdf · doi:10.1007/s00454-009-9176-0

published in Discrete & Computational Geometry 42(1), 71-93 (Springer Science and Business Media LLC)

openalex publication_date 2009/04/23 · crossref created 2009/04/23 · crossref issued 2009/04/24 · crossref published 2009/04/24 · crossref published-online 2009/04/24 · crossref published-print 2009/07/01 · crossref deposited 2021/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29 · crossref indexed 2026/08/07

Citations

• On the Local Behavior of Spaces of Natural Images
• Computing Persistent Homology
• Topological Persistence and Simplification
• Local Algebra
• Hyperbolic Groups

Cited by

• Betti numbers in multidimensional persistent homology are stable functions
• Computing Multidimensional Persistence
• The Persistence Space in Multidimensional Persistent Homology
• Finiteness of rank invariants of multidimensional persistent homology groups
• Stable Comparison of Multidimensional Persistent Homology Groups with Torsion
• Necessary conditions for discontinuities of multidimensional persistent Betti numbers
• Topological pattern recognition for point cloud data
• An output-sensitive algorithm for persistent homology
• Topology and data
• One-dimensional reduction of multidimensional persistent homology
• A fast algorithm for constructing topological structure in large data
• Stratifying Multiparameter Persistent Homology
• Estimating Multidimensional Persistent Homology Through a Finite Sampling
• Topological data analysis [wikipedia]