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

P. Pilarczyk, P. Real, Advances in Computational Mathematics 41 (2014) 253–275.


Journal Article | Published
Author
Abstract
We introduce algorithms for the computation of homology, cohomology, and related operations on cubical cell complexes, using the technique based on a chain contraction from the original chain complex to a reduced one that represents its homology. This work is based on previous results for simplicial complexes, and uses Serre’s diagonalization for cubical cells. An implementation in C++ of the introduced algorithms is available at http://www.pawelpilarczyk.com/chaincon/ together with some examples. The paper is self-contained as much as possible, and is written at a very elementary level, so that basic knowledge of algebraic topology should be sufficient to follow it.
Publishing Year
Date Published
2014-01-01
Journal Title
Advances in Computational Mathematics
Acknowledgement
This research was partially supported from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE – Programa Operacional Factores de Compe titividade (POFC) and from the Portuguese national funds through Fundacaoparaa Ciencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645(ref. FCT PTDC/MAT/098871/2008), as well as from the funds distributed through the European Science Foundation (ESF) Research Networking Programme on “Applied and Computational Algebraic Topology” (ACAT). P.Real was additionally supported by the Spanish Ministry of Science and Innovation, project no. MTM2009-12716.
Volume
41
Issue
1
Page
253 - 275
IST-REx-ID
451

Cite this

Pilarczyk P, Real P. Computation of cubical homology, cohomology, and (co)homological operations via chain contraction. Advances in Computational Mathematics. 2014;41(1):253-275. doi:10.1007/s10444-014-9356-1
Pilarczyk, P., & Real, P. (2014). Computation of cubical homology, cohomology, and (co)homological operations via chain contraction. Advances in Computational Mathematics, 41(1), 253–275. https://doi.org/10.1007/s10444-014-9356-1
Pilarczyk, Pawel, and Pedro Real. “Computation of Cubical Homology, Cohomology, and (Co)Homological Operations via Chain Contraction.” Advances in Computational Mathematics 41, no. 1 (2014): 253–75. https://doi.org/10.1007/s10444-014-9356-1.
P. Pilarczyk and P. Real, “Computation of cubical homology, cohomology, and (co)homological operations via chain contraction,” Advances in Computational Mathematics, vol. 41, no. 1, pp. 253–275, 2014.
Pilarczyk P, Real P. 2014. Computation of cubical homology, cohomology, and (co)homological operations via chain contraction. Advances in Computational Mathematics. 41(1), 253–275.
Pilarczyk, Pawel, and Pedro Real. “Computation of Cubical Homology, Cohomology, and (Co)Homological Operations via Chain Contraction.” Advances in Computational Mathematics, vol. 41, no. 1, Kluwer, 2014, pp. 253–75, doi:10.1007/s10444-014-9356-1.
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