A Note on the Homotopy Type of the Alexander Dual
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 s...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_01795376_v52_n1_p34_Minian |
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todo:paper_01795376_v52_n1_p34_Minian2023-10-03T15:08:33Z A Note on the Homotopy Type of the Alexander Dual Minian, E.G. Rodríguez, J.T. Alexander duality Bier spheres Deleted joins Homotopy types Lattices Simplicial complexes 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. Fil:Minian, E.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01795376_v52_n1_p34_Minian |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Alexander duality Bier spheres Deleted joins Homotopy types Lattices Simplicial complexes |
| spellingShingle |
Alexander duality Bier spheres Deleted joins Homotopy types Lattices Simplicial complexes Minian, E.G. Rodríguez, J.T. A Note on the Homotopy Type of the Alexander Dual |
| topic_facet |
Alexander duality Bier spheres Deleted joins Homotopy types Lattices Simplicial complexes |
| description |
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. |
| format |
JOUR |
| author |
Minian, E.G. Rodríguez, J.T. |
| author_facet |
Minian, E.G. Rodríguez, J.T. |
| author_sort |
Minian, E.G. |
| title |
A Note on the Homotopy Type of the Alexander Dual |
| title_short |
A Note on the Homotopy Type of the Alexander Dual |
| title_full |
A Note on the Homotopy Type of the Alexander Dual |
| title_fullStr |
A Note on the Homotopy Type of the Alexander Dual |
| title_full_unstemmed |
A Note on the Homotopy Type of the Alexander Dual |
| title_sort |
note on the homotopy type of the alexander dual |
| url |
http://hdl.handle.net/20.500.12110/paper_01795376_v52_n1_p34_Minian |
| work_keys_str_mv |
AT minianeg anoteonthehomotopytypeofthealexanderdual AT rodriguezjt anoteonthehomotopytypeofthealexanderdual AT minianeg noteonthehomotopytypeofthealexanderdual AT rodriguezjt noteonthehomotopytypeofthealexanderdual |
| _version_ |
1782027479498620928 |