Lamination duale à un arbre réel

Hilion, Arnaud¹

¹ LATP - UMR 6632 Université Aix-Marseille 3 Avenue de l’escadrille Normandie-Niémen 13397 Marseille Cedex 20 (France)

Séminaire de théorie spectrale et géométrie, Tome 24 (2005-2006), pp. 9-21.

Résumé

Nous présentons des résultats reliant un arbre réel muni d’une action par isométries du groupe libre, sa lamination duale et les courants portés par cette dernière.

Détail

DOI : 10.5802/tsg.237

Bibliographie

[1] Bestvina, M. $ℝ$-trees in topology, geometry, and group theory, Handbook of geometric topology, North-Holland, Amsterdam, 2002, pp. 55-91 | Zbl | MR

[2] Casson, A.; Bleiler, S. Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, 9, Cambridge University Press, Cambridge, 1988 | Zbl | MR

[3] Cohen, M.; Lustig, M. Very small group actions on $\mathbf{R}$-trees and Dehn twist automorphisms, Topology, Volume 34 (1995) no. 3, pp. 575-617 | Zbl | MR

[4] Coulbois, T.; Hilion, A.; Levitt, G.; Lustig, M. (en préparation)

[5] Coulbois, T.; Hilion, A.; Lustig, M. $ℝ$-trees and laminations for free groups III : Currents and dual $ℝ$-tree metrics (2005) (preprint available on http://junon.u-3mrs.fr/hilion/)

[6] Coulbois, T.; Hilion, A.; Lustig, M. Non uniquely ergodic R-trees are topologically determined by their algebraic lamination (2005) (preprint available on http://junon.u-3mrs.fr/hilion/)

[7] Coulbois, T.; Hilion, A.; Lustig, M. $ℝ$-trees and laminations for free groups I : Algebraic laminations (2006) (arXiv :math.GR/0609416)

[8] Coulbois, T.; Hilion, A.; Lustig, M. $ℝ$-trees and laminations for free groups II : The dual lamination of an $ℝ$-tree (2007) (arXiv :math.GR/0702281)

[9] Fathi, A.; Laudenbach, F.; Poenaru, V. Travaux de Thurston sur les surfaces, Astérisque, 66-67, Société Mathématique de France, Paris, 1976 | Zbl | mathdoc-id

[10] Kapovich, I. Currents on free groups (2005) (ArXiv :math.GR/0311053) | MR

[11] Kapovich, I.; Lustig, M. The actions of $Out\left(F_k\right)$ on the boundary of Outer space and on the space of currents : minimal sets and equivariant incompatibility (2006) (arXiv :math/0605548) | Zbl

[12] Kapovich, Michael Hyperbolic manifolds and discrete groups, Progress in Mathematics, 183, Birkhäuser Boston Inc., Boston, MA, 2001 | Zbl | MR

[13] Keynes, H.; Newton, D. A “minimal”, non-uniquely ergodic interval exchange transformation, Math. Z., Volume 148 (1976) no. 2, pp. 101-105 | Zbl | EuDML

[14] Levitt, G.; Lustig, M. Irreducible automorphisms of $F_n$ have north-south dynamics on compactified outer space, J. Inst. Math. Jussieu, Volume 2 (2003), pp. 59-72 | Zbl | MR

[15] Lustig, M. $ℝ$-trees - currents - laminations : a delicate relationship (2007) (preprint)

[16] Shalen, P. Dendrology of groups : an introduction, Essays in group theory (Math. Sci. Res. Inst. Publ.), Volume 8, Springer, New York, 1987, pp. 265-319 | Zbl | MR

[17] Veech, W. Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem $\mathrm{mod}2$, Trans. Amer. Math. Soc., Volume 140 (1969), pp. 1-33 | Zbl | MR

[18] Vogtmann, K. Automorphisms of free groups and outer space, Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000), Volume 94 (2002), pp. 1-31 | Zbl | MR