Fixed point properties in the space of marked groups

Details Fixed point properties in the space of marked groups Fixed point properties in the space of marked groups

2008-03-18

arxiv.org/abs/0803.2592v3

Limits of graphs in group theory and computer science Proc. Special semester at Centre Bernoulli (Lausanne), Jan-June 2007, Go

Mathematics

Group Theory

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

Scientific paper

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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