paper

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

arXiv:math/0306306 · doi:10.2140/gt.2004.8.1427

Abstract

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R^n-trees. We first prove that Sela's limit groups do have a free action on an R^n-tree. We then prove that a finitely generated group having a free action on an R^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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper39.abs.html

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