The cubical cohomology ring: an algorithmic approach

DOI10.1007/s10208-012-9138-4zbMath1350.55002OpenAlexW2052543097MaRDI QIDQ385447

Marian Mrozek, Tomasz Kaczynski

Publication date: 2 December 2013

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-012-9138-4

zbMATH Keywords

cohomology ring\(S\)-complexcombinatorial cubical complexcoreduction algorithmcup-product formula

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to algebraic topology (55-04) Polytopes and polyhedra (52B99) Chain complexes (category-theoretic aspects), dg categories (18G35) Other homology theories in algebraic topology (55N35) Products and intersections in homology and cohomology (55N45)

Related Items

Computing cup products in \(\mathbb{Z}_2\)-cohomology of 3D polyhedral complexes ⋮ Computation of cubical homology, cohomology, and (co)homological operations via chain contraction ⋮ Computation of Cubical Steenrod Squares ⋮ Unnamed Item ⋮ Cohomology ring of tree braid groups and exterior face rings

Uses Software

• HAP
• RedHom
• CHomP
• Dionysus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coreduction homology algorithm for inclusions and persistent homology
• Coreduction homology algorithm for regular CW-complexes
• Distributed computation of coverage in sensor networks by homological methods
• On the local behavior of spaces of natural images
• Coreduction homology algorithm
• On the algebra of cubes
• Computation of cohomology operations on finite simplicial complexes
• Computational homology
• Homologie singulière des espaces fibrés. Applications
• Verified Homology Computations for Nodal Domains
• Electromagnetic Theory and Computation