2-frieze patterns and the cluster structure of the space of polygons
Algebraic Geometry
2011-07-19 v5 Combinatorics
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.
Keywords
Cite
@article{arxiv.1008.3359,
title = {2-frieze patterns and the cluster structure of the space of polygons},
author = {Sophie Morier-Genoud and Valentin Ovsienko and Serge Tabachnikov},
journal= {arXiv preprint arXiv:1008.3359},
year = {2011}
}
Comments
36 pages, 4 figures, minor changes from the previous versions; references added (v2), section 5.5 added (v3), picture added (v4)