The covering type of closed surfaces and minimal triangulations

The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex...

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Detalles Bibliográficos
Autores principales: Borghini, E., Minian, E.G.
Formato: JOUR
Materias:
Covering type
Minimal triangulations
Surfaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00973165_v166_n_p1_Borghini
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00973165_v166_n_p1_Borghini
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spelling todo:paper_00973165_v166_n_p1_Borghini2023-10-03T14:56:47Z The covering type of closed surfaces and minimal triangulations Borghini, E. Minian, E.G. Covering type Minimal triangulations Surfaces The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex homotopy equivalent to X. In this article we compute the covering type of all closed surfaces. Our results completely settle a problem posed by Karoubi and Weibel, and shed more light on the relationship between the topology of surfaces and the number of vertices of minimal triangulations from a homotopy point of view. © 2019 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00973165_v166_n_p1_Borghini
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Covering type
Minimal triangulations
Surfaces
spellingShingle Covering type
Minimal triangulations
Surfaces
Borghini, E.
Minian, E.G.
The covering type of closed surfaces and minimal triangulations
topic_facet Covering type
Minimal triangulations
Surfaces
description The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex homotopy equivalent to X. In this article we compute the covering type of all closed surfaces. Our results completely settle a problem posed by Karoubi and Weibel, and shed more light on the relationship between the topology of surfaces and the number of vertices of minimal triangulations from a homotopy point of view. © 2019 Elsevier Inc.
format JOUR
author Borghini, E.
Minian, E.G.
author_facet Borghini, E.
Minian, E.G.
author_sort Borghini, E.
title The covering type of closed surfaces and minimal triangulations
title_short The covering type of closed surfaces and minimal triangulations
title_full The covering type of closed surfaces and minimal triangulations
title_fullStr The covering type of closed surfaces and minimal triangulations
title_full_unstemmed The covering type of closed surfaces and minimal triangulations
title_sort covering type of closed surfaces and minimal triangulations
url http://hdl.handle.net/20.500.12110/paper_00973165_v166_n_p1_Borghini
work_keys_str_mv AT borghinie thecoveringtypeofclosedsurfacesandminimaltriangulations
AT minianeg thecoveringtypeofclosedsurfacesandminimaltriangulations
AT borghinie coveringtypeofclosedsurfacesandminimaltriangulations
AT minianeg coveringtypeofclosedsurfacesandminimaltriangulations
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