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2-frieze patterns and the cluster structure of the space of polygons

Sophie Morier-Genoud;  Valentin Ovsienko;  Serge Tabachnikov — 2012

Annales de l’institut Fourier

We study 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of n -gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus 0 curves with n marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.

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