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...
| Autores: | , , , |
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| 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 |
| 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. |
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