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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Minian, Elias Gabriel
Publicado: 2014
Materias:
Alexander duality
Bier spheres
Deleted joins
Homotopy types
Lattices
Simplicial complexes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v52_n1_p34_Minian
http://hdl.handle.net/20.500.12110/paper_01795376_v52_n1_p34_Minian
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01795376_v52_n1_p34_Minian
record_format dspace
spelling paper:paper_01795376_v52_n1_p34_Minian2023-06-08T15:19:29Z A Note on the Homotopy Type of the Alexander Dual Minian, Elias Gabriel 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v52_n1_p34_Minian 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, Elias Gabriel
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.
author Minian, Elias Gabriel
author_facet Minian, Elias Gabriel
author_sort Minian, Elias Gabriel
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
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v52_n1_p34_Minian
http://hdl.handle.net/20.500.12110/paper_01795376_v52_n1_p34_Minian
work_keys_str_mv AT minianeliasgabriel anoteonthehomotopytypeofthealexanderdual
AT minianeliasgabriel noteonthehomotopytypeofthealexanderdual
_version_ 1768542360215486464

Ejemplares similares