Finitely Presented Groups Acting on Trees

M. J. Dunwoody

Finitely Presented Groups Acting on Trees

Geometric Topology 2022-02-23 v3 Group Theory

Authors: M. J. Dunwoody

Abstract

It is shown that for any action of a finitely presented group $G$ on an $\R$ -tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there is no global fixed point, then $G$ has a non-trivial action on a simplcial $\R$ -tree.

Keywords

algebraic group actions group actions finite group theory

Cite

@article{arxiv.1203.6019,
  title  = {Finitely Presented Groups Acting on Trees},
  author = {M. J. Dunwoody},
  journal= {arXiv preprint arXiv:1203.6019},
  year   = {2022}
}

Comments

18 pages, 8 figures. An incorrect example has been removed and the main result corrected

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