A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls

We prove a generalization of a result of Dong and Santos-Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an...

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Detalles Bibliográficos
Autor principal: Minian, Elias Gabriel
Publicado: 2016
Materias:
Alexander dual
Combinatorial manifolds
Simplicial complexes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00973165_v138_n_p155_Capitelli
http://hdl.handle.net/20.500.12110/paper_00973165_v138_n_p155_Capitelli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00973165_v138_n_p155_Capitelli2023-06-08T15:09:48Z A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls Minian, Elias Gabriel Alexander dual Combinatorial manifolds Simplicial complexes We prove a generalization of a result of Dong and Santos-Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally when considering the double duals of standard balls and spheres. © 2015 Elsevier Inc. Fil:Minian, E.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00973165_v138_n_p155_Capitelli http://hdl.handle.net/20.500.12110/paper_00973165_v138_n_p155_Capitelli
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 dual
Combinatorial manifolds
Simplicial complexes
spellingShingle Alexander dual
Combinatorial manifolds
Simplicial complexes
Minian, Elias Gabriel
A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls
topic_facet Alexander dual
Combinatorial manifolds
Simplicial complexes
description We prove a generalization of a result of Dong and Santos-Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-pure counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally when considering the double duals of standard balls and spheres. © 2015 Elsevier Inc.
author Minian, Elias Gabriel
author_facet Minian, Elias Gabriel
author_sort Minian, Elias Gabriel
title A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls
title_short A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls
title_full A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls
title_fullStr A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls
title_full_unstemmed A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls
title_sort generalization of a result of dong and santos-sturmfels on the alexander dual of spheres and balls
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00973165_v138_n_p155_Capitelli
http://hdl.handle.net/20.500.12110/paper_00973165_v138_n_p155_Capitelli
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AT minianeliasgabriel generalizationofaresultofdongandsantossturmfelsonthealexanderdualofspheresandballs
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