# Rips Induction: Index of the dual lamination of an $\R$-tree

@article{Coulbois2010RipsII,
title={Rips Induction: Index of the dual lamination of an \$\R\$-tree},
author={Thierry Coulbois and Arnaud Hilion},
journal={arXiv: Group Theory},
year={2010}
}
• Published 2010
• Mathematics
• arXiv: Group Theory
Let $T$ be a $\R$-tree in the boundary of the Outer Space CV$_N$, with dense orbits. The $Q$-index of $T$ is defined by means of the dual lamination of $T$. It is a generalisation of the Euler-Poincar\'e 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. Combining our results on the $\CQ$-index with… Expand

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