Geodesic
Rips induction: index of the dual lamination of an $\mathbb{R}$-tree
Thierry Coulbois1 ; Arnaud Hilion1
1Aix-Marseille Université, Marseille, France
Groups, geometry, and dynamics, Tome 8 (2014) no. 1, pp. 97-134

Voir la notice de l'article provenant de la source EMS Press

DOI

Let T be a R-tree in the boundary of the Outer Space CVN​, with dense orbits. The Q-index of T is defined by means of the dual lamination of T. It is a generalisation of the Poincaré Lefschetz index of a foliation on a surface. We prove that the Q-index of T is bounded above by 2N−2, and we study the case of equality. The main tool is to develop the Rips machine in order to deal with systems of isometries on compact R-trees.
DOI : 10.4171/ggd/218
Classification : 20-XX
Mots-clés : R-trees, Outer Space, Rips machine

Thierry Coulbois  1   ; Arnaud Hilion  1

1 Aix-Marseille Université, Marseille, France 
Thierry Coulbois; Arnaud Hilion. Rips induction: index of the dual lamination of an $\mathbb{R}$-tree. Groups, geometry, and dynamics, Tome 8 (2014) no. 1, pp. 97-134. doi: 10.4171/ggd/218
@article{10_4171_ggd_218,
     author = {Thierry Coulbois and Arnaud Hilion},
     title = {Rips induction: index of the dual lamination of an $\mathbb{R}$-tree},
     journal = {Groups, geometry, and dynamics},
     pages = {97--134},
     year = {2014},
     volume = {8},
     number = {1},
     doi = {10.4171/ggd/218},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/218/}
}
TY  - JOUR
AU  - Thierry Coulbois
AU  - Arnaud Hilion
TI  - Rips induction: index of the dual lamination of an $\mathbb{R}$-tree
JO  - Groups, geometry, and dynamics
PY  - 2014
SP  - 97
EP  - 134
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/218/
DO  - 10.4171/ggd/218
ID  - 10_4171_ggd_218
ER  - 
%0 Journal Article
%A Thierry Coulbois
%A Arnaud Hilion
%T Rips induction: index of the dual lamination of an $\mathbb{R}$-tree
%J Groups, geometry, and dynamics
%D 2014
%P 97-134
%V 8
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/218/
%R 10.4171/ggd/218
%F 10_4171_ggd_218

Cité par Sources :