Strong Homotopy Types, Nerves and Collapses

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse....

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Detalles Bibliográficos
Autores principales: Barmak, Jonathan A., Minian, Elias Gabriel
Publicado: 2012
Materias:
Collapses
Finite spaces
Nerves
Non-evasiveness
Posets
Simple homotopy types
Simplicial actions
Simplicial complexes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v47_n2_p301_Barmak
http://hdl.handle.net/20.500.12110/paper_01795376_v47_n2_p301_Barmak
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01795376_v47_n2_p301_Barmak
record_format dspace
spelling paper:paper_01795376_v47_n2_p301_Barmak2023-06-08T15:19:28Z Strong Homotopy Types, Nerves and Collapses Barmak, Jonathan A. Minian, Elias Gabriel Collapses Finite spaces Nerves Non-evasiveness Posets Simple homotopy types Simplicial actions Simplicial complexes We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relationship with the nerves of the complexes. From this theory we derive new results for studying simplicial collapsibility with a different point of view. We analyze vertex-transitive simplicial G-actions and prove a particular case of the Evasiveness conjecture for simplicial complexes. Moreover, we reduce the general conjecture to the class of minimal complexes. We also strengthen a result of V. Welker on the barycentric subdivision of collapsible complexes. We obtain this and other results on collapsibility of polyhedra by means of the characterization of the different notions of collapses in terms of finite topological spaces. © 2011 Springer Science+Business Media, LLC. Fil:Barmak, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Minian, E.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v47_n2_p301_Barmak http://hdl.handle.net/20.500.12110/paper_01795376_v47_n2_p301_Barmak
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Collapses
Finite spaces
Nerves
Non-evasiveness
Posets
Simple homotopy types
Simplicial actions
Simplicial complexes
spellingShingle Collapses
Finite spaces
Nerves
Non-evasiveness
Posets
Simple homotopy types
Simplicial actions
Simplicial complexes
Barmak, Jonathan A.
Minian, Elias Gabriel
Strong Homotopy Types, Nerves and Collapses
topic_facet Collapses
Finite spaces
Nerves
Non-evasiveness
Posets
Simple homotopy types
Simplicial actions
Simplicial complexes
description We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relationship with the nerves of the complexes. From this theory we derive new results for studying simplicial collapsibility with a different point of view. We analyze vertex-transitive simplicial G-actions and prove a particular case of the Evasiveness conjecture for simplicial complexes. Moreover, we reduce the general conjecture to the class of minimal complexes. We also strengthen a result of V. Welker on the barycentric subdivision of collapsible complexes. We obtain this and other results on collapsibility of polyhedra by means of the characterization of the different notions of collapses in terms of finite topological spaces. © 2011 Springer Science+Business Media, LLC.
author Barmak, Jonathan A.
Minian, Elias Gabriel
author_facet Barmak, Jonathan A.
Minian, Elias Gabriel
author_sort Barmak, Jonathan A.
title Strong Homotopy Types, Nerves and Collapses
title_short Strong Homotopy Types, Nerves and Collapses
title_full Strong Homotopy Types, Nerves and Collapses
title_fullStr Strong Homotopy Types, Nerves and Collapses
title_full_unstemmed Strong Homotopy Types, Nerves and Collapses
title_sort strong homotopy types, nerves and collapses
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v47_n2_p301_Barmak
http://hdl.handle.net/20.500.12110/paper_01795376_v47_n2_p301_Barmak
work_keys_str_mv AT barmakjonathana stronghomotopytypesnervesandcollapses
AT minianeliasgabriel stronghomotopytypesnervesandcollapses
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