Limit groups and groups acting freely on $\bbR^n$-trees
数字图书馆
2007-05-23 v1
摘要
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.
引用
@article{arxiv.cs/0307049,
title = {Limit groups and groups acting freely on $\bbR^n$-trees},
author = {Vincent Guirardel},
journal= {arXiv preprint arXiv:cs/0307049},
year = {2007}
}