Fixed point properties in the space of marked groups

Yves Stalder (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Property (FRA); Uniform actions; ultralimits; Property (T); Property (FRA).

Domaines: Théorie des groupes [math.GR]

Yves Stalder. Fixed point properties in the space of marked groups. Goulnara Arzhantseva and Alain Valette. Limits of graphs in group theory and computer science Proc. Special semester at Centre Bernoulli (Lausanne), Jan-June 2007, Presses polytechniques et universitaires romandes, pp.171--182, 2009. ⟨hal-00264907v3⟩