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| HAL : hal-00000428, version 4 |
| arXiv : math.GR/0306306 |
| DOI : 10.2140/gt.2004.8.1427 |
| Fiche détaillée |  Récupérer au format |
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| Geometry and Toplogy 8 (2004) 1427–1470 |
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| Versions disponibles : | v1 (20-06-2003) | v2 (30-06-2003) | v3 (01-07-2003) | v4 (21-07-2003) |
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| Limit groups and groups acting freely on R^n-trees. |
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| Vincent Guirardel 1 |
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| (2004) |
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| We give a simple proof of the finite presentation of Sela's limit groupsby using free actions on $\bbR^n$-trees.We first prove that Sela's limit groups do have a free action on an $\bbR^n$-tree.We then prove that a finitely generated group having a free action on an $\bbR^n$-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic groups.As a corollary, such a group is finitely presented, has a finite classifying space,its abelian subgroups are finitely generated and contains onlyfinitely many conjugacy classes of non-cyclic maximal abelian subgroups. |
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| 1 : | Laboratoire Émile Picard (LEP) |
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CNRS : UMR5580 – Université Paul Sabatier - Toulouse III |
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| Domaine | : | Mathématiques/Théorie des groupes Mathématiques/Topologie géométrique Mathématiques/Logique |
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| limit groups – Lambda-trees |
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| hal-00000428, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00000428 | |
| oai:hal.archives-ouvertes.fr:hal-00000428 | |
| Contributeur : Vincent Guirardel | |
| Soumis le : Lundi 21 Juillet 2003, 15:15:30 | |
| Dernière modification le : Jeudi 15 Janvier 2009, 16:56:00 | |
