Artículo
Minian, E.G.; Rodríguez, J.T. "A Note on the Homotopy Type of the Alexander Dual" (2014) Discrete and Computational Geometry. 52(1):34-43
Estamos trabajando para incorporar este artículo al repositorio
Consulte la política de Acceso Abierto del editor
Abstract:
We investigate the homotopy type of the Alexander dual of a simplicial complex. It is known that in general the homotopy type of K does not determine the homotopy type of its dual K*. We construct for each finitely presented group G, a simply connected simplicial complex K such that π1(K*) = G and study sufficient conditions on K for K* to have the homotopy type of a sphere. We extend the simplicial Alexander duality to the more general context of reduced lattices and relate this construction with Bier spheres using deleted joins of lattices. Finally we introduce an alternative dual, in the context of reduced lattices, with the same homotopy type as the Alexander dual but smaller and simpler to compute. © 2014 Springer Science+Business Media New York.
Registro:
| Documento: | Artículo |
| Título: | A Note on the Homotopy Type of the Alexander Dual |
| Autor: | Minian, E.G.; Rodríguez, J.T. |
| Filiación: | Departamento de Matemática-IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina |
| Palabras clave: | Alexander duality; Bier spheres; Deleted joins; Homotopy types; Lattices; Simplicial complexes |
| Año: | 2014 |
| Volumen: | 52 |
| Número: | 1 |
| Página de inicio: | 34 |
| Página de fin: | 43 |
| DOI: | http://dx.doi.org/10.1007/s00454-014-9606-5 |
| Título revista: | Discrete and Computational Geometry |
| Título revista abreviado: | Discrete Comput. Geom. |
| ISSN: | 01795376 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v52_n1_p34_Minian |
Referencias:
- Barmak, J.A., Algebraic topology of finite topological spaces and applications (2011) Lecture Notes in Mathematics, 2032. , Springer, Berlin
- Barmak, J.A., Minian, E.G., Strong homotopy types, nerves and collapses (2012) Discrete Comput. Geom., 47 (2), pp. 301-328
- Barr, M., A duality on simplicial complexes (2002) Georgian Math. J., 9 (4), pp. 601-605
- Bier, T., (1992) A remark on Alexander duality and the disjunct join, , Unpublished
- Björner, A., Tancer, M., Combinatorial Alexander duality. A short and elementary proof (2009) Discrete Comput. Geom., 42 (4), pp. 586-593
- Cohen, M.M., (1970) A Course in Simple Homotopy Theory, , Heidelberg: Springer
- de Longueville, M., Bier spheres and barycentric subdivision (2004) J. Comb. Theory Ser. A, 105, pp. 355-357
- Dong, X., Alexander duality for projections of polytopes (2002) Topology, 41, pp. 1109-1121
- Hatcher, A., (2002) Algebraic Topology, , Cambridge: Cambridge University Press
- Kozlov, D., Simple homotopy types of hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes (2006) Topol. Appl., 153, pp. 2445-2454
- Matoušek, J., (2003) Using the Borsuk-Ulam Theorem. Lectures on Topological Methods in Combinatorics and Geometry, Written in Cooperation with A. Björner and G. Ziegler, , Heidelberg: Springer
Citas:
---------- APA ----------
Minian, E.G. & Rodríguez, J.T. (2014) . A Note on the Homotopy Type of the Alexander Dual. Discrete and Computational Geometry, 52(1), 34-43.http://dx.doi.org/10.1007/s00454-014-9606-5
---------- CHICAGO ----------
Minian, E.G., Rodríguez, J.T. "A Note on the Homotopy Type of the Alexander Dual" . Discrete and Computational Geometry 52, no. 1 (2014) : 34-43.http://dx.doi.org/10.1007/s00454-014-9606-5
---------- MLA ----------
Minian, E.G., Rodríguez, J.T. "A Note on the Homotopy Type of the Alexander Dual" . Discrete and Computational Geometry, vol. 52, no. 1, 2014, pp. 34-43.http://dx.doi.org/10.1007/s00454-014-9606-5
---------- VANCOUVER ----------
Minian, E.G., Rodríguez, J.T. A Note on the Homotopy Type of the Alexander Dual. Discrete Comput. Geom. 2014;52(1):34-43.http://dx.doi.org/10.1007/s00454-014-9606-5
