Kazhdan and Haagerup properties from the median viewpoint

By Indira Chatterji, Cornelia Drutu, Frédéric Haglund. 2007

125 citations recorded by the source corpus.

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 and Steger.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/971b3ffcf63dac49b15b28ab3becbfbe33296dc4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Yves Cornulier
2. Yves Stalder
3. Alessandro Sisto
4. Alain Valette
5. Jason A. Behrstock
6. Damian Osajda

In Mathematical Physics

1. Alessandro Sisto
2. Mark F. Hagen
3. Jason A. Behrstock
4. Damian Osajda
5. Yves Cornulier
6. Yves Stalder
7. Alain Valette
8. Jérémie Chalopin

Citations in the corpus

• Weakly Modular Graphs and Nonpositive Curvature (2014, background): “uently many classical groups were cubulated, that is they were shown to act geometrically on CAT(0) cubical complexes; see e.g., [Wis04,Wis11]. Cubulated groups posses many nice properties; see e.g., [CDH10]. Using the so-called special cube complexes [HW08], by cubulating fundamental groups of 3{ma”
• Hierarchically hyperbolic spaces II: Combination theorems and the distance formula (2015, background): “t median spaces/groups admitting factor systems are hierarchically hyperbolic? Presumably, a positive answer to Question B would involve the measured wallspace structure on median spaces discussed in [CDH10]. One would have to develop an analogue of the contact graph of a cube complex to serve as th”
• PROPER ACTIONS OF WREATH PRODUCTS AND GENERALIZATIONS (2009, methodology): “Thus, by [ CDH , Theorem 5.1], Y can be turned into a space with measured walls (Y;W;B;„), in the sense of [CMV], such that G acts by automorphisms of spaces with walls [CDH, Deflnition 3.5].”