Fixed point properties in the space of marked groups
classification
🧮 math.GR
keywords
groupsactionsfixedisometricmarkedpointspacecommon
read the original 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.
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