Artículo
Borghini, E.; Minian, E.G. "The covering type of closed surfaces and minimal triangulations" (2019) Journal of Combinatorial Theory. Series A. 166:1-10
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | The covering type of closed surfaces and minimal triangulations |
| Autor: | Borghini, E.; Minian, E.G. |
| Filiación: | Departamento de Matemática, IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina |
| Palabras clave: | Covering type; Minimal triangulations; Surfaces |
| Año: | 2019 |
| Volumen: | 166 |
| Página de inicio: | 1 |
| Página de fin: | 10 |
| DOI: | http://dx.doi.org/10.1016/j.jcta.2019.02.005 |
| Título revista: | Journal of Combinatorial Theory. Series A |
| Título revista abreviado: | J. Comb. Theory Ser. A |
| ISSN: | 00973165 |
| CODEN: | JCBTA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00973165_v166_n_p1_Borghini |
Referencias:
- Brehm, U., Kühnel, W., Combinatorial manifolds with few vertices (1987) Topology, 26, pp. 465-473
- Brehm, U., Kühnel, W., 15-vertex triangulations of an 8-manifold (1992) Math. Ann., 294, pp. 167-193
- Heawood, P.J., Map-colour theorem (1890) Quart. J. Pure Appl. Math., 24, pp. 332-338
- Huneke, J.P., A minimum-vertex triangulation (1978) J. Combin. Theory Ser. B, 24, pp. 258-266
- Jungerman, M., Ringel, G., Minimal triangulations on orientable surfaces (1980) Acta Math., 145, pp. 121-154
- Karoubi, M., Weibel, C., On the covering type of a space (2016) Enseign. Math., 62, pp. 457-474
- Lutz, F., Triangulated Manifolds with Few Vertices and Vertex-Transitive Group Actions (1999) Berichte aus der Mathematik, , Dissertation, Technischen Universität Berlin, Berlin Verlag Shaker Aachen
- Lutz, F., Combinatorial 3-manifolds with 10 vertices (2008) Beitr. Algebra Geom., 49, pp. 97-106
- Ringel, G., Wie man die geschlossenen nichtorientierbaren Flächen in möglichst wenig Dreiecke zerlegen kann (1955) Math. Ann., 130, pp. 317-326
Citas:
---------- APA ----------
Borghini, E. & Minian, E.G. (2019) . The covering type of closed surfaces and minimal triangulations. Journal of Combinatorial Theory. Series A, 166, 1-10.http://dx.doi.org/10.1016/j.jcta.2019.02.005
---------- CHICAGO ----------
Borghini, E., Minian, E.G. "The covering type of closed surfaces and minimal triangulations" . Journal of Combinatorial Theory. Series A 166 (2019) : 1-10.http://dx.doi.org/10.1016/j.jcta.2019.02.005
---------- MLA ----------
Borghini, E., Minian, E.G. "The covering type of closed surfaces and minimal triangulations" . Journal of Combinatorial Theory. Series A, vol. 166, 2019, pp. 1-10.http://dx.doi.org/10.1016/j.jcta.2019.02.005
---------- VANCOUVER ----------
Borghini, E., Minian, E.G. The covering type of closed surfaces and minimal triangulations. J. Comb. Theory Ser. A. 2019;166:1-10.http://dx.doi.org/10.1016/j.jcta.2019.02.005
