Polyhedral Realization of a Thurston Compactification

Matthieu Gendulphe; Yohei Komori

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 1, page 95-114
  • ISSN: 0240-2963

Abstract

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Let Σ 3 - be the connected sum of three real projective planes. We realize the Thurston compactification of the Teichmüller space Teich ( Σ 3 - ) as a simplex in P ( ℝ 4 ) .

How to cite

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Gendulphe, Matthieu, and Komori, Yohei. "Polyhedral Realization of a Thurston Compactification." Annales de la faculté des sciences de Toulouse Mathématiques 23.1 (2014): 95-114. <http://eudml.org/doc/275367>.

@article{Gendulphe2014,
abstract = {Let $\Sigma _3^-$ be the connected sum of three real projective planes. We realize the Thurston compactification of the Teichmüller space $\mathsf \{Teich\}(\Sigma _3^-)$ as a simplex in $\mathbf\{P\}(\mathbb\{R\}^4)$.},
author = {Gendulphe, Matthieu, Komori, Yohei},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Teichmüller space; Thurston compactification},
language = {eng},
number = {1},
pages = {95-114},
publisher = {Université Paul Sabatier, Toulouse},
title = {Polyhedral Realization of a Thurston Compactification},
url = {http://eudml.org/doc/275367},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Gendulphe, Matthieu
AU - Komori, Yohei
TI - Polyhedral Realization of a Thurston Compactification
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 1
SP - 95
EP - 114
AB - Let $\Sigma _3^-$ be the connected sum of three real projective planes. We realize the Thurston compactification of the Teichmüller space $\mathsf {Teich}(\Sigma _3^-)$ as a simplex in $\mathbf{P}(\mathbb{R}^4)$.
LA - eng
KW - Teichmüller space; Thurston compactification
UR - http://eudml.org/doc/275367
ER -

References

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  1. Bonahon (F.).— The geometry of Teichmüller space via geodesic currents. Invent. Math., 92(1), p. 139-162 (1988). Zbl0653.32022MR931208
  2. Fathi (A.), Laudenbach (F.), and Poénaru (V.).— Travaux de Thurston sur les surfaces, Astérisque, vol. 66-67. Société Mathématique de France (1991). Zbl0446.57018MR1134426
  3. Gendulphe (M.).— Paysage systolique des surfaces hyperboliques de caractéristique -1. available at http://matthieu.gendulphe.com. 
  4. Hamenstädt (U.).— Parametrizations of Teichmüller space and its Thurston boundary. In Geometric analysis and nonlinear partial differential equations, p. 81-88. Springer (2003). Zbl1044.32005
  5. Scharlemann (M.).— The complex of curves on nonorientable surfaces. J. London Math. Soc. (2), 25(1), p. 171-184, 1982. Zbl0479.57005MR645874
  6. Schmutz (P.).— Une paramétrisation de l’espace de Teichmüller de genre g donnée par 6 g - 5 géodésiques explicites. In Séminaire de Théorie Spectrale et Géométrie, No. 10, Année 1991-1992, volume 10, p. 59-64. Univ. Grenoble I (1992). Zbl0773.53017MR1715913
  7. Schmutz (P.).— Die Parametrisierung des Teichmüllerraumes durch geodätische Längenfunktionen. Comment. Math. Helv., 68(2), p. 278-288 (1993). Zbl0790.30036MR1214232
  8. Thurston (W. P.).— On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc., 19(2), p. 417-431 (1988). Zbl0674.57008MR956596

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