English

Fixed point properties in the space of marked groups

Group Theory 2010-01-29 v3

Abstract

We explain, following Gromov, how to produce uniform isometric actions of groups starting from isometric actions without fixed point, using common ultralimits techniques. This gives in particular a simple proof of a result by Shalom: Kazhdan's property (T) defines an open subset in the space of marked finitely generated groups.

Keywords

Cite

@article{arxiv.0803.2592,
  title  = {Fixed point properties in the space of marked groups},
  author = {Yves Stalder},
  journal= {arXiv preprint arXiv:0803.2592},
  year   = {2010}
}

Comments

The only modification from previous version is section numbering, in order to agree with the published version

R2 v1 2026-06-21T10:22:22.550Z