Kazhdan and Haagerup properties from the median viewpoint

Details Kazhdan and Haagerup properties from the median viewpoint Kazhdan and Haagerup properties from the median viewpoint

2007-04-29

arxiv.org/abs/0704.3749v4

Mathematics

Group Theory

final version

Scientific paper

We prove the existence of a close connection between spaces with measured walls and median metric spaces. We then relate properties (T) and Haagerup (a-T-menability) to actions on median spaces and on spaces with measured walls. This allows us to explore the relationship between the classical properties (T) and Haagerup and their versions using affine isometric actions on $L^p$-spaces. It also allows us to answer an open problem on a dynamical characterization of property (T), generalizing results of Robertson-Steger.

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