Making Sullivan Algebras Minimal Through Chain Contractions

In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, taking as input a (nonminimal) Sullivan algebra A with an ordered finite set of generators preserving the filtration defined on A, we obtain as output a minimal Sullivan algebra...

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Detalles Bibliográficos
Autores: Garvin, Antonio, González Díaz, Rocío, Marco, Miguel Ángel, Medrano Garfia, Belén
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/110821
Acceso en línea:https://hdl.handle.net/11441/110821
https://doi.org/10.1007/s00009-020-01670-9
Access Level:acceso abierto
Palabra clave:Sullivan algebras
Minimal models
Chain homotopy
Chain contractions
AT-model
Descripción
Sumario:In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, taking as input a (nonminimal) 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.