Abstract
In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, taking as input a (non-minimal) Sullivan algebra A with an ordered finite set of generators preserving the filtration defined on A, we obtain as output a minimal Sullivan algebra with the same rational cohomology as A. This algorithm is a kind of modified AT-model algorithm used, in the past, to compute a chain contraction providing other kinds of topological information such as (co)homology, cup products on cohomology and persistent homology.
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R. Gonzalez-Diaz, B. Medrano: Partially supported by MICINN, FEDER/UE under grant PID2019-107339GB-100. Antonio Garvín: partially supported by the Spanish MINECO and ERDF grant MTM2016-78647-P and by the Junta de Andalucía grant FQM-213.
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Garvin, A., Gonzalez-Diaz, R., Marco, M.A. et al. Making Sullivan Algebras Minimal Through Chain Contractions. Mediterr. J. Math. 18, 43 (2021). https://doi.org/10.1007/s00009-020-01670-9
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DOI: https://doi.org/10.1007/s00009-020-01670-9