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

Sophie Morier-Genoud; Valentin Ovsienko; Serge Tabachnikov

doi:10.5802/aif.2713

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

Sophie Morier-Genoud, Valentin Ovsienko, Serge Tabachnikov

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28 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	937-987
Number of pages	51
Journal	Annales de l'Institut Fourier
Volume	62
Issue number	3
DOIs	https://doi.org/10.5802/aif.2713
State	Published - 2012

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

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

Abstract

All Science Journal Classification (ASJC) codes

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