Email this article Computing Intersection Numbers and Bases of Cohomology Groups for Triangulated Closed Three-Dimensional Manifolds
- Authors: Yakovlev E.I.1, Epifanov V.Y.2
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Affiliations:
- Department of Fundamental Mathematics, Faculty of Informatics, Mathematics, and Computer Science
- Department of Algebra, Geometry and Discrete Mathematics, Institute of Information Technology, Mathematics and Mechanics
- Issue: Vol 40, No 5 (2019)
- Pages: 690-698
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204547
- DOI: https://doi.org/10.1134/S1995080219050226
- ID: 204547
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Abstract
We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing intersection numbers of 1- and 2-dimensional cycles are developed. Using these algorithms it is possible to construct a basis of the cohomology group from a given basis of the homology group of complementary dimension.
About the authors
E. I. Yakovlev
Department of Fundamental Mathematics, Faculty of Informatics, Mathematics, and Computer Science
Author for correspondence.
Email: eyakovlev@hse.ru
Russian Federation, ul. Bol’shaya Pecherskaya 25/12, Nizhny Novgorod, 603155
V. Y. Epifanov
Department of Algebra, Geometry and Discrete Mathematics, Institute of Information Technology, Mathematics and Mechanics
Author for correspondence.
Email: vepifanov92@gmail.com
Russian Federation, Nizhny Novgorod, 603950
