Homology, Homotopy and Applications

Volume 5 (2003)

Number 2

Volume of a Workshop at Stanford University

Computing homology

Pages: 233 – 256

DOI: https://dx.doi.org/10.4310/HHA.2003.v5.n2.a8


Tomasz Kaczynski (Département de mathématiques et d’informatique, Université de Sherbrooke, Québec, Canada)

Konstantin Mischaikow (Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, GA. U.S.A.)

Marian Mrozek (Institute of Computer Science, Jagiellonian University, Kraków, Poland)


The aim of this paper is to provide a short introduction to computational homology based on cubical complexes. The discussed topics include cubical complexes, a reduction algorithm for computing homology of finitely generated chain complexes, and an algorithmic construction of homology of continuous maps via multivalued acyclic representations.


homology computation, algorithm, cubical complex, representable set, mulitivalued map

2010 Mathematics Subject Classification

, 65D17. Primary 55-04. Secondary 52B05, 54C60.

Published 1 January 2003