The Cylinder of a Relation and Generalized Versions of the Nerve Theorem

We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen’s Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theore...

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Detalles Bibliográficos
Autores principales: Fernández, X., Minian, E.G.
Formato: INPR
Materias:
Finite topological spaces
Nerve
Posets
Quillen’s Theorem A
Relations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01795376_v_n_p_Fernandez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01795376_v_n_p_Fernandez
record_format dspace
spelling todo:paper_01795376_v_n_p_Fernandez2023-10-03T15:08:34Z The Cylinder of a Relation and Generalized Versions of the Nerve Theorem Fernández, X. Minian, E.G. Finite topological spaces Nerve Posets Quillen’s Theorem A Relations We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen’s Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections. © 2018, Springer Science+Business Media, LLC, part of Springer Nature. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01795376_v_n_p_Fernandez
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Finite topological spaces
Nerve
Posets
Quillen’s Theorem A
Relations
spellingShingle Finite topological spaces
Nerve
Posets
Quillen’s Theorem A
Relations
Fernández, X.
Minian, E.G.
The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
topic_facet Finite topological spaces
Nerve
Posets
Quillen’s Theorem A
Relations
description We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen’s Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
format INPR
author Fernández, X.
Minian, E.G.
author_facet Fernández, X.
Minian, E.G.
author_sort Fernández, X.
title The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
title_short The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
title_full The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
title_fullStr The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
title_full_unstemmed The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
title_sort cylinder of a relation and generalized versions of the nerve theorem
url http://hdl.handle.net/20.500.12110/paper_01795376_v_n_p_Fernandez
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AT minianeg thecylinderofarelationandgeneralizedversionsofthenervetheorem
AT fernandezx cylinderofarelationandgeneralizedversionsofthenervetheorem
AT minianeg cylinderofarelationandgeneralizedversionsofthenervetheorem
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