Limit groups and groups acting freely on $\bbR^n$-trees
<|reference_start|>Limit groups and groups acting freely on $\bbR^n$-trees: We give a simple proof of the finite presentation of Sela's limit groups by 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 only finitely many conjugacy classes of non-cyclic maximal abelian subgroups.<|reference_end|>
@article{guirardel2003limit,
    title={Limit groups and groups acting freely on $\bbR^n$-trees},
    author={Vincent Guirardel},
    journal={arXiv preprint arXiv:cs/0307049},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0307049},
    primaryClass={cs.DL}
}