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Computing homology.

Kaczynski, Tomasz, Mischaikow, Konstantin, Mrozek, Marian (2003)

Homology, Homotopy and Applications

Cubical approximation and computation of homology

William Kalies, Konstantin Mischaikow, Greg Watson (1999)

Banach Center Publications

The purpose of this article is to introduce a method for computing the homology groups of cellular complexes composed of cubes. We will pay attention to issues of storage and efficiency in performing computations on large complexes which will be required in applications to the computation of the Conley index. The algorithm used in the homology computations is based on a local reduction procedure, and we give a subquadratic estimate of its computational complexity. This estimate is rigorous in two...

Homology of representable sets

Marian Mrozek, Bogdan Batko (2010)

Annales Polonici Mathematici

We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.

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