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We propose a new framework to build databases of surfaces with rich mathematical structure. Our approach is based on ideas that come from Teichmuller 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.

Parametrised databases of surfaces based on Teichmüller theory