Parametrised databases of surfaces based on Teichmüller theory

Gina Lusares; Armando Rodado Amaris

doi:10.4067/S0719-06462016000100006

Authors

Gina Lusares Departamento de Estadistica, Universidad de Valparaiso, Blanco 951, Valparaiso, Chile
Armando Rodado Amaris Departamento de Ciencias Exactas, Universidad de los Lagos, Av. Fuchslocher 1305, Osorno, Chile

DOI:

https://doi.org/10.4067/S0719-06462016000100006

Keywords:

Database of Surfaces, Design Teichmüller space, Moduli Space of Riemann surfaces, Canonical cell decomposition of Riemann surfaces, Teichmüller surfaces descriptor

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.