Abstract
We give a simple proof of the finite presentation of Sela’s limit groups by using free actions on –trees. We first prove that Sela’s limit groups do have a free action on an –tree. We then prove that a finitely generated group having a free action on an –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.
Citation
Vincent Guirardel. "Limit groups and groups acting freely on $\mathbb{R}^n$–trees." Geom. Topol. 8 (3) 1427 - 1470, 2004. https://doi.org/10.2140/gt.2004.8.1427
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