Computation of cubical homology, cohomology, and (co)homological operations via chain contraction

DOI10.1007/s10444-014-9356-1zbMath1312.55005OpenAlexW2053395628WikidataQ59388586 ScholiaQ59388586MaRDI QIDQ2017610

Paweł Pilarczyk, Pedro Real

Publication date: 23 March 2015

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/xmlui/handle/11441/38719

zbMATH Keywords

softwarealgorithmcohomologyhomologycup productSmith normal formcubical complexcell complexcomputational homologychain homotopychain contractionAlexander-Whitney coproduct

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to algebraic topology (55-04) Chain complexes in algebraic topology (55U15) Other homology theories in algebraic topology (55N35) Abstract complexes in algebraic topology (55U05) Duality in applied homological algebra and category theory (aspects of algebraic topology) (55U30)

Related Items (9)

Efficient construction of 2-chains representing a basis of \(H_{2}(\overline {\Omega }, \partial {\Omega }; \mathbb {Z})\) ⋮ Allowing cycles in discrete Morse theory ⋮ Connectivity calculus of fractal polyhedrons ⋮ Homology groups of cubical sets ⋮ Parallel homological calculus for 3D binary digital images ⋮ Inducing a map on homology from a correspondence ⋮ Computation of Cubical Steenrod Squares ⋮ ChainCon ⋮ Searching combinatorial optimality using graph-based homology information

Uses Software

• CAPD
• CHomP

Cites Work

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