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

By Sophie Morier-Genoud, Valentin Ovsienko, Serge Tabachnikov. 2010

58 citations recorded by the source corpus.

We study the space of 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f99b1c68563f953ebf591797f86023c8ba42a102

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Liouville–Arnold integrability of the pentagram map on closed polygons (2011, background): “ter algebra mutations, and an explicit formula for the iterations of Tis calculated1. The structure of cluster manifold on the space C nand the related notion of 2-frieze pattern are investigated in [10]. 2 Integrability on the space of twisted n-gons In this section, we explain the proof of the mai”
Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics (2015, background): “x1 x1 1 1 1 1 ··· 1.6 From inﬁnite friezes to the variety of tame friezes In this section, we explain the structure of algebraic variety on the set of Coxeter’s friezes. The following idea is used in [MGOT12]. We consider the formal inﬁnite frieze pattern F(Ai)i∈Z, where (Ai)i∈Z is a sequence of ind”