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

Sophie Morier-Genoud, Valentin Ovsienko, Serge Tabachnikov

Research output: Contribution to journalArticle

17 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 languageEnglish (US)
Pages (from-to)937-987
Number of pages51
JournalAnnales de l'Institut Fourier
Volume62
Issue number3
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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