@inproceedings{gazull2025-characterization_homology_bases,
    author = "Gazull, Yann-Situ and Gonzalez-Lorenzo, Aldo and Bac, Alexandra",
    title = "Characterization of the Computed Homology and Cohomology Bases",
    booktitle = "International Conference on Discrete Geometry and Mathematical Morphology",
    pages = "163--177",
    year = "2025",
    organization = "Springer",
    doi = "10.1007/978-3-032-09544-2\_12",
    url = "https://dx.doi.org/10.1007/978-3-032-09544-2\_12",
    abstract = "Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric objects). The present paper provides a characterization of the class of homology bases that are computed by standard algorithmic methods. The proof of this characterization relies on the Homological Discrete Vector Field, a combinatorial structure for computing homology, which encompasses several standard methods (persistent homology, tri-partitions, Smith Normal Form, discrete Morse theory). These results refine the combinatorial homology theory and provide novel ideas to gain more control over the computation of homology generators."
}