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Computing The Cubical Cohomology Ring (Extended Abstract)


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Opened Access Computing The Cubical Cohomology Ring (Extended Abstract)
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Author: Kaczynski, Tomasz
Dlotko, Pawel
Mrozek, Marian
Date: 2010
Published in: Image-A : Applicable Mathematics in Image Engineering, 1 (3), 137-142
Document type: Article
Abstract: The goal of this work is to establish a new algorithm for computing the cohomology ring of cubical complexes. The cubical structure enables an explicit recurrence formula for the cup product. We derive this formula and, next, show how to extend the Mrozek and Batko [7] homology coreduction algorithm to the cohomology ring structure. The implementation of the algorithm is a work in progress. This research is aimed at applications in electromagnetism and in image processing, among other fields.
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