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Cubo (Temuco)

versão On-line ISSN 0719-0646

Cubo vol.18 no.1 Temuco  2016

http://dx.doi.org/10.4067/S0719-06462016000100006 

 

Parametrised databases of surfaces based on Teichmüller theory

 

Armando Rodado Amaris 1, Gina Lusares 2

1 Departamento de Ciencias Exactas, Universidad de los Lagos, Av. Fuchslocher 1305, Osorno, Chile

2 Departamento de Estadistica, Universidad de Valparaiso, Blanco 951, Valparaiso, Chile armando.rodado@ulagos.cl, gina.lusares@postgrado.uv.cl


ABSTRACT

We propose a new framework to build databases of surfaces with rich mathematical structure. Our approach is based on ideas that come from Teichmüller and moduli space of closed Riemann surfaces theory, and the problem of finding a canonical and explicit cell decomposition of these spaces. Databases built using our approach will have a graphical underlying structure, which can be built from a single graph by contraction and expansion moves.

Keywords and Phrases: Database of Surfaces Design Teichmüller space Moduli Space of Riemann surfaces Canonical cell decomposition of Riemann surfaces Teichmüller surfaces descriptor.

2010 AMS Mathematics Subject Classification:


RESUMEN

Proponemos un nuevo marco teórico para construir bases de datos de superficies con rica estructura matemática. Nuestro enfoque está basado en ideas que vienen de teoría de espacios de Teichmüller y espacios módulares de superficies de Riemann cerradas, y el problema de encontrar una descomposición celular canónica y explícita de estos espacios. Las bases de datos construidas usando nuestro enfoque tendrán una estructura gráfica subyacente, la que se puede construir a partir de un solo grafo por movimientos de expansión y contracción.


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