Simplicial Lusternik-Schnirelmann category
The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many not...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/106288 |
| Acceso en línea: | https://hdl.handle.net/11441/106288 https://doi.org/10.5565/PUBLMAT6311909 |
| Access Level: | acceso abierto |
| Palabra clave: | Lusternik{Schnirelmann category strong homotopy type geometric realization Whitehead formulation of category graph arboricity |
| Sumario: | The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many notions and results of alge- braic topology which are costumary in the classical theory of Lusternik{Schnirelmann category. Also we compare the simplicial category of a complex with the LS-category of its geometric realization and we discuss the simplicial analogue of the Whitehead formulation of the LS-category. |
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