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

By Sophie Morier-Genoud, Valentin Ovsienko and Serge Tabachnikov

Abstract

International audienceWe 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

Topics: [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]
Publisher: Association des Annales de l'Institut Fourier
Year: 2012
OAI identifier: oai:HAL:hal-00864650v1
Provided by: Hal-Diderot

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