Limit groups and groups acting freely on $\bbR^n$-trees

Details Limit groups and groups acting freely on $\bbR^n$-trees Limit groups and groups acting freely on $\bbR^n$-trees

2003-07-21

arxiv.org/abs/cs/0307049v1

Computer Science

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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.

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