Effective homological computations on finite topological spaces

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 genera...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing Vol. 34; no. 1; pp. 33 - 56
Main Authors: Cuevas-Rozo, Julián, Lambán, Laureano, Romero, Ana, Sarria, Humberto
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2023
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Combinatorial analysis
Computer Hardware
Computer Science
Fields (mathematics)
Homology
Linear algebra
Original Paper
Software
Symbolic and Algebraic Manipulation
Theory of Computation
Topology
68W30
55-04
Discrete vector fields
Homology
Finite topological spaces
Simplicial complexes
55U15
06A07
ISSN:0938-1279, 1432-0622
Online Access:Get full text
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Summary: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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ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-020-00462-8