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

 

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Opened Access Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
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Author: Pilarczyk, Pawel
Real Jurado, Pedro
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2015
Published in: Advances in Computational Mathematics, 41 (1), 253-275.
Document type: Article
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.
Cite: Pilarczyk, P. y Real Jurado, P. (2015). Computation of cubical homology, cohomology, and (co)homological operations via chain contraction. Advances in Computational Mathematics, 41, 253-275.
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Format: PDF

URI: http://hdl.handle.net/11441/38719

DOI: http://dx.doi.org/10.1007/s10444-014-9356-1

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