Limit groups and groups acting freely on R^n-trees.

Vincent Guirardel (1)

1 LEP - Laboratoire Émile Picard

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.

Mots clés: limit groups; Lambda-trees

Domaines: Théorie des groupes [math.GR]; Topologie géométrique [math.GT]; Logique [math.LO]

Vincent Guirardel. Limit groups and groups acting freely on R^n-trees.. Geometry and Toplogy, 2004, 8, pp.1427-1470. ⟨10.2140/gt.2004.8.1427⟩. ⟨hal-00000428v4⟩