, Volume 13, Issue 5, pp 789-818,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 26 Oct 2012

The Cubical Cohomology Ring: An Algorithmic Approach

Abstract

A cohomology ring algorithm in a dimension-independent framework of combinatorial cubical complexes is developed with the aim of applying it to the topological analysis of high-dimensional data. This approach is convenient in the cup-product computation and motivated, among others, by interpreting pixels or voxels in digital images as cubes. The S-complex theory and so called co-reductions are adopted to build a cohomology ring algorithm speeding up the algebraic computations.

Communicated by Gunnar Carlsson.