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Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 1/2023

26-11-2020 | Original Paper

Effective homological computations on finite topological spaces

Authors: Julián Cuevas-Rozo, Laureano Lambán, Ana Romero, Humberto Sarria

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 1/2023

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Abstract

The study of topological invariants of finite topological spaces is relevant because they can be used as models of a wide class of topological spaces, including regular CW-complexes. In this work, we present a new module for the Kenzo system that allows the computation of homology groups with generators of finite topological spaces in different situations. Our algorithms combine new constructive versions of well-known results about topological spaces with combinatorial methods used on finite spaces. In the particular case of h-regular spaces, effective and reasonably efficient methods are implemented and the technique of discrete vector fields is applied in order to improve the previous algorithms.
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Footnotes
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Metadata
Title
Effective homological computations on finite topological spaces
Authors
Julián Cuevas-Rozo
Laureano Lambán
Ana Romero
Humberto Sarria
Publication date
26-11-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 1/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00462-8

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