---
_id: '451'
abstract:
- lang: eng
  text: 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.
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. '
article_processing_charge: No
article_type: original
author:
- first_name: Pawel
  full_name: Pilarczyk, Pawel
  id: 3768D56A-F248-11E8-B48F-1D18A9856A87
  last_name: Pilarczyk
- first_name: Pedro
  full_name: Real, Pedro
  last_name: Real
citation:
  ama: Pilarczyk P, Real P. Computation of cubical homology, cohomology, and (co)homological
    operations via chain contraction. <i>Advances in Computational Mathematics</i>.
    2014;41(1):253-275. doi:<a href="https://doi.org/10.1007/s10444-014-9356-1">10.1007/s10444-014-9356-1</a>
  apa: Pilarczyk, P., &#38; Real, P. (2014). Computation of cubical homology, cohomology,
    and (co)homological operations via chain contraction. <i>Advances in Computational
    Mathematics</i>. Kluwer. <a href="https://doi.org/10.1007/s10444-014-9356-1">https://doi.org/10.1007/s10444-014-9356-1</a>
  chicago: Pilarczyk, Pawel, and Pedro Real. “Computation of Cubical Homology, Cohomology,
    and (Co)Homological Operations via Chain Contraction.” <i>Advances in Computational
    Mathematics</i>. Kluwer, 2014. <a href="https://doi.org/10.1007/s10444-014-9356-1">https://doi.org/10.1007/s10444-014-9356-1</a>.
  ieee: P. Pilarczyk and P. Real, “Computation of cubical homology, cohomology, and
    (co)homological operations via chain contraction,” <i>Advances in Computational
    Mathematics</i>, vol. 41, no. 1. Kluwer, pp. 253–275, 2014.
  ista: 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.
  mla: Pilarczyk, Pawel, and Pedro Real. “Computation of Cubical Homology, Cohomology,
    and (Co)Homological Operations via Chain Contraction.” <i>Advances in Computational
    Mathematics</i>, vol. 41, no. 1, Kluwer, 2014, pp. 253–75, doi:<a href="https://doi.org/10.1007/s10444-014-9356-1">10.1007/s10444-014-9356-1</a>.
  short: P. Pilarczyk, P. Real, Advances in Computational Mathematics 41 (2014) 253–275.
date_created: 2018-12-11T11:46:33Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2026-09-09T13:17:12Z
day: '01'
doi: 10.1007/s10444-014-9356-1
extern: '1'
fulldoi: https://doi.org/10.1007/s10444-014-9356-1
intvolume: '        41'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://idus.us.es/xmlui/handle/11441/38719
month: '01'
oa: 1
oa_version: None
page: 253 - 275
publication: Advances in Computational Mathematics
publication_identifier:
  eissn:
  - 1572-9044
  issn:
  - 1019-7168
publication_status: published
publisher: Kluwer
publist_id: '7371'
status: public
title: Computation of cubical homology, cohomology, and (co)homological operations
  via chain contraction
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 41
year: '2014'
...