Core and intersection number for group actions on trees

Details Core and intersection number for group actions on trees Core and intersection number for group actions on trees

2004-07-12

arxiv.org/abs/math/0407206v2

Annales scientifiques de l'Ecole normale sup\'erieure 38, 6 (2005) 847-888

Mathematics

Group Theory

Scientific paper

10.1016/j.ansens.2005.11.001

We present the construction of some kind of "convex core" for the product of two actions of a group on $\bbR$-trees. This geometric construction allows to generalize and unify the intersection number of two curves or of two measured foliations on a surface, Scott's intersection number of splittings, and the apparition of surfaces in Fujiwara-Papasoglu's construction of the JSJ splitting. In particular, this construction allows a topological interpretation of the intersection number analogous to the definition for curves in surfaces. As an application of this construction, we prove that an irreducible automorphism of the free group whose stable and unstable trees are geometric, is actually induced a pseudo-Anosov homeomorphism on a surface.

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