Handbook of Teichmüller Theory, Volume I

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pp: 507–540

DOI: 10.4171/029-1/13

On the moduli space of singular euclidean surfaces

Marc Troyanov[1]

(1) Ecole Polytechnique Fédérale de Lausanne, Switzerland

The goal of this article is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.

Keywords: Singular Euclidean surface, representation, Abelian representation, developing map, holonomy