Some remarks on Morse theory for posets, homological Morse theory and finite manifolds

We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related to R. Forman’s discrete Morse theory for CW-complexes and generalizes Forman a...

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Detalhes bibliográficos
Autor: Minian, Elias Gabriel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/19957
Acesso em linha:http://hdl.handle.net/11336/19957
Access Level:acceso abierto
Palavra-chave:Morse Theory
Finite Spaces
Posets
Homology
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related to R. Forman’s discrete Morse theory for CW-complexes and generalizes Forman and Chari’s results on the face posets of regular CW-complexes. We also introduce a homological variant of the theory that can be used to study the topology of triangulable homology manifolds by means of their order triangulations.