The number of critical elements of discrete Morse functions on non-compact surfaces

This paper is focused on looking for links between the topology of a connected and non-compact surface with finitely many ends and any proper discrete Morse function which can be defined on it. More precisely, we study the non-compact surfaces which admit a proper discrete Morse function with a give...

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Detalles Bibliográficos
Autores: Ayala Gómez, Rafael, Fernández Fernández, Luis Manuel, Vilches Alarcón, José Antonio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/183598
Acceso en línea:https://hdl.handle.net/11441/183598
https://doi.org/10.1016/j.topol.2009.04.045
Access Level:acceso abierto
Palabra clave:Non-compact simplicial complex
Critical element
Gradient vector field
Gradient path
Descripción
Sumario:This paper is focused on looking for links between the topology of a connected and non-compact surface with finitely many ends and any proper discrete Morse function which can be defined on it. More precisely, we study the non-compact surfaces which admit a proper discrete Morse function with a given number of critical elements. In particular, given any of these surfaces, we obtain an optimal discrete Morse function on it, that is, with the minimum possible number of critical elements.