# Kazhdan and Haagerup properties from the median viewpoint

Abstract : 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.
Type de document :
Article dans une revue
Advances in Mathematics, Elsevier, 2010, pp.Volume 225, Issue 2 (2010), 882 - 921
Domaine :

https://hal.archives-ouvertes.fr/hal-00471046
Contributeur : Indira Chatterji <>
Soumis le : mercredi 7 avril 2010 - 14:15:51
Dernière modification le : jeudi 3 mai 2018 - 15:32:06

### Identifiants

• HAL Id : hal-00471046, version 1
• ARXIV : 0704.3749

### Citation

Indira Chatterji, Cornelia Drutu, Frederic Haglund. Kazhdan and Haagerup properties from the median viewpoint. Advances in Mathematics, Elsevier, 2010, pp.Volume 225, Issue 2 (2010), 882 - 921. 〈hal-00471046〉

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