Coreduction homology algorithm for regular CW-complexes

DOI10.1007/s00454-010-9303-yzbMath1229.55001OpenAlexW2085831227WikidataQ112198350 ScholiaQ112198350MaRDI QIDQ635750

Tomasz Kaczynski, Paweł Dłotko, Thomas Wanner, Marian Mrozek

Publication date: 23 August 2011

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-010-9303-y

zbMATH Keywords

CW-complexesreduction methodshomology algorithmnon-uniform cubical setsS-complexes

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to algebraic topology (55-04) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Software, source code, etc. for problems pertaining to manifolds and cell complexes (57-04)

Related Items (13)

Allowing cycles in discrete Morse theory ⋮ The cubical cohomology ring: an algorithmic approach ⋮ Discrete Morse theoretic algorithms for computing homology of complexes and maps ⋮ Homological Shape Analysis Through Discrete Morse Theory ⋮ On $\varepsilon $ approximations of persistence diagrams ⋮ Computational homology of \(n\)-types ⋮ Computing multiparameter persistent homology through a discrete Morse-based approach ⋮ Rigorous cubical approximation and persistent homology of continuous functions ⋮ Dual complexes of cubical subdivisions of \({\mathbb{R}}^{n}\) ⋮ Topological microstructure analysis using persistence landscapes ⋮ Detecting critical regions in multidimensional data sets ⋮ Homology Computation During an Incremental Construction Process ⋮ Homology of cellular structures allowing multi-incidence

Uses Software

• Homology
• CAPD

Cites Work

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• Čech type approach to computing homology of maps
• Coreduction homology algorithm for inclusions and persistent homology
• Homology algorithm based on acyclic subspace
• Topology-guided sampling of nonhomogeneous random processes
• Coreduction homology algorithm
• Homology computation by reduction of chain complexes
• Computing Betti numbers via combinatorial Laplacians
• Computing homology
• Computational homology
• Topological persistence and simplification
• \(\mathbb{Z}_2\)-homology of weak \((p-2)\)-faceless \(p\)-pseudomanifolds may be computed in \(O(n)\) time
• Probabilistic validation of homology computations for nodal domains
• Verified Homology Computations for Nodal Domains
• Random Fields and Geometry
• Probabilistic and numerical validation of homology computations for nodal domains

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