The Cubical Cohomology Ring: An Algorithmic Approach
Tomasz Kaczyński, Marian Mrożek · Foundations of Computational Mathematics · 2012
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.