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

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 and some examples are available at http://www.pawelpilarczyk.com/chaincon/. 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. Keywords algorithm · software · homology · cohomology · computational homology · cup product · Alexander-Whitney coproduct · chain homotopy · chain contraction · cubical complex Mathematics Subject Classification (2000) 55N35 · 52B99 · 55U15 · 55U30 · 55-04

• Type: Journal
• Year: 2015
• Where: ADCM
• Authors: Pawel Pilarczyk, Pedro Real
• Keywords: ADCM 2015, Database