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

Abstract

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.

36 pages, 4 figures, minor changes from the previous versions; references added (v2), section 5.5 added (v3), picture added (v4)