### The rank of actions on $R$-trees

Damien Gaboriau, Gilbert Levitt (1995)

Annales scientifiques de l'École Normale Supérieure

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Damien Gaboriau, Gilbert Levitt (1995)

Annales scientifiques de l'École Normale Supérieure

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Vincent Guirardel (2008)

Annales de l’institut Fourier

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We study actions of finitely generated groups on $\mathbb{R}$-trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing together actions of simple types: actions on simplicial trees, actions on lines, and actions coming from measured foliations on $2$-orbifolds. This extends results by Sela and Rips-Sela. However, their results are misstated, and we give a counterexample to their...

Bernd Brinkmann, Frank Herrlich (1994)

Compositio Mathematica

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Mladen Bestvina, Mark Feighn (1991)

Inventiones mathematicae

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Clay, Matt (2005)

Algebraic & Geometric Topology

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Vincent Guirardel (2000)

Annales scientifiques de l'École Normale Supérieure

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Forester, Max (2002)

Geometry & Topology

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F.A. Muntaner-Batle, Miquel Rius-Font (2008)

Discussiones Mathematicae Graph Theory

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We study the structure of path-like trees. In order to do this, we introduce a set of trees that we call expandable trees. In this paper we also generalize the concept of path-like trees and we call such generalization generalized path-like trees. As in the case of path-like trees, generalized path-like trees, have very nice labeling properties.