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

Sophie Morier-Genoud[1]; Valentin Ovsienko[2]; Serge Tabachnikov[3]

  • [1] Institut de Mathématiques de Jussieu UMR 7586 Université Pierre et Marie Curie 4, place Jussieu, case 247 75252 Paris Cedex 05
  • [2] CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
  • [3] Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 937-987
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Morier-Genoud, Sophie, Ovsienko, Valentin, and Tabachnikov, Serge. "2-frieze patterns and the cluster structure of the space of polygons." Annales de l’institut Fourier 62.3 (2012): 937-987. <http://eudml.org/doc/251031>.

@article{Morier2012,
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.},
affiliation = {Institut de Mathématiques de Jussieu UMR 7586 Université Pierre et Marie Curie 4, place Jussieu, case 247 75252 Paris Cedex 05; CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France; Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA},
author = {Morier-Genoud, Sophie, Ovsienko, Valentin, Tabachnikov, Serge},
journal = {Annales de l’institut Fourier},
keywords = {Frieze patterns; Coxeter-Conway friezes; moduli space; cluster algebra; pentagram map; frieze patterns},
language = {eng},
number = {3},
pages = {937-987},
publisher = {Association des Annales de l’institut Fourier},
title = {2-frieze patterns and the cluster structure of the space of polygons},
url = {http://eudml.org/doc/251031},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Morier-Genoud, Sophie
AU - Ovsienko, Valentin
AU - Tabachnikov, Serge
TI - 2-frieze patterns and the cluster structure of the space of polygons
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 937
EP - 987
AB - 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.
LA - eng
KW - Frieze patterns; Coxeter-Conway friezes; moduli space; cluster algebra; pentagram map; frieze patterns
UR - http://eudml.org/doc/251031
ER -

References

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