English

No-splitting property and boundaries of random groups

Geometric Topology 2021-04-02 v1 Group Theory

Abstract

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.

Keywords

Cite

@article{arxiv.0904.3854,
  title  = {No-splitting property and boundaries of random groups},
  author = {François Dahmani and Vincent Guirardel and Piotr Przytycki},
  journal= {arXiv preprint arXiv:0904.3854},
  year   = {2021}
}

Comments

20 pages

R2 v1 2026-06-21T12:54:47.606Z