Limit groups and groups acting freely on R^n-trees.
Guirardel, Vincent
HAL, hal-00000428 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  Lambda-trees,  limit groups,  20E08, 20F05, 20F10,  [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR],  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT],  [MATH.MATH-LO]Mathematics [math]/Logic [math.LO] 
@article{hal-00000428,
     author = {Guirardel, Vincent},
     title = {Limit groups and groups acting freely on R^n-trees.},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00000428}
}

Guirardel, Vincent. Limit groups and groups acting freely on R^n-trees.. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00000428/