Cubical approximation and computation of homology

Volume 47 / 1999

William Kalies, Konstantin Mischaikow, Greg Watson Banach Center Publications 47 (1999), 115-131 DOI: 10.4064/-47-1-115-131

Abstract

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 dimensions, and we conjecture its validity in higher dimensions.

Authors

  • William Kalies
  • Konstantin Mischaikow
  • Greg Watson

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