Fixed point properties in the space of marked groups

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.

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

References in corpus (1)

• Quasi-isometry rigidity of groups

Cited by in corpus (4)

• A local characterization of Kazhdan projections and applications
• The Lipschitz metric on deformation spaces of $G$-trees
• On Property (FA) for wreath products
• New examples of groups acting on real trees