Titlebook: Quantum Triangulations; Moduli Space, Quantu Mauro Carfora,Annalisa Marzuoli Book 2017Latest edition Springer International Publishing AG 2

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Triangulated Surfaces and Polyhedral Structures,art by recalling the relevant definitions from Piecewise–Linear (PL) geometry, (for which we refer freely to Rourke and Sanderson (Introduction to piecewise-linear topology. Springer, New York, 1982) and Thurston (Three-dimensional geometry and topology. Volume 1 (edited by S. Levy). Princeton Unive

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Singular Euclidean Structures and Riemann Surfaces,vertices of the triangulation. In this chapter we show that around any such a vertex we can introduce complex coordinates in terms of which we can write down the conformal conical metric, locally parametrizing the singular structure of (.., .). This makes available a powerful dictionary between 2-di

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The Quantum Geometry of Polyhedral Surfaces: Variations on Strings and All That,rtheless proves useful for illustrating the interplay between quantum field theory, the moduli space of Riemann surfaces, and the properties of polyhedral surfaces which are the . of this LNP. At the root of this interplay lies 2D quantum gravity. It is well known that such a theory allows for two c

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