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| HAL: hal-00002181, version 2 |
| arXiv: math.GR/0407206 |
| DOI: 10.1016/j.ansens.2005.11.001 |
| Detailed view |  Export this paper |
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| Annales scientifiques de l'Ecole normale supérieure 38, 6 (2005) 847-888 |
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| Available versions: | v1 (2004-07-08) | v2 (2004-07-21) |
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| Core and intersection number for group actions on trees |
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| Vincent Guirardel 1 |
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| (2005) |
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| 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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| 1: | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| Subject | : | Mathematics/Group Theory |
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| hal-00002181, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00002181 | |
| oai:hal.archives-ouvertes.fr:hal-00002181 | |
| From: Vincent Guirardel | |
| Submitted on: Wednesday, 21 July 2004 09:20:27 | |
| Updated on: Thursday, 15 January 2009 16:50:40 | |
