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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.54 no.2 Bogotá jul./dez. 2020 Epub 05-Mar-2021
https://doi.org/10.15446/recolma.v54n2.93844
Artículos originales
Coverings of Configurations, Prime Configurations, and Orbiconfigurations
Recubrimientos de configuraciones, configuraciones primas, y orbiconfiguraciones
1 St. Martin's University, Lacey, United States
This exploratory paper considers the notion of a covering of a configuration and G-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot G-cover other configurations, before considering orbiconfigurations. These are a generalized notion of a configuration in the spirit of an orbifold. We derive some specific results as to when configurations are prime as well as considering when an orbiconfiguration is bad - that is, when it cannot be G-covered by a configuration. A number of open questions are posited within.
Keywords: Configuration; covering; orbiconfiguration
Este artículo exploratorio considera la noción de un recubrimiento de una configuración y los G-recubrimientos, recubrimientos que son cocientes de una acción de grupo semi-regular. Consideramos las configuraciones primas, aquellas que no pueden G-recubrir otras configuraciones, antes de considerar las orbiconfiguraciones. Se trata de una noción generalizada de una configuración en el espíritu de un orbifold. Derivamos algunos resultados específicos de cuándo las configuraciones son primas. Tenemos en cuenta cuándo una orbiconfiguración es mala, es decir, cuándo no puede ser recubierta por una configuración. En el artículo se plantean una serie de preguntas abiertas.
Palabras clave: Configuración; orbiconfiguraciones; recubrimientos
References
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Received: April 01, 2020; Accepted: August 13, 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
