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

Sophie Morier-Genoud, Valentin Ovsienko, Serge Tabachnikov

Research output: Contribution to journalArticle

16 Citations (Scopus)

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 - Oct 12 2012

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Polygon
Projective plane
Moduli Space
Vector space
Genus
Curve

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Morier-Genoud, Sophie ; Ovsienko, Valentin ; Tabachnikov, Serge. / 2-frieze patterns and the cluster structure of the space of polygons. In: Annales de l'Institut Fourier. 2012 ; Vol. 62, No. 3. pp. 937-987.
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2-frieze patterns and the cluster structure of the space of polygons. / Morier-Genoud, Sophie; Ovsienko, Valentin; Tabachnikov, Serge.

In: Annales de l'Institut Fourier, Vol. 62, No. 3, 12.10.2012, p. 937-987.

Research output: Contribution to journalArticle

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