Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-02T05:11:58.865Z Has data issue: false hasContentIssue false
  • English
  • Français

Spaces with measured walls, the Haagerup property and property (T)

Published online by Cambridge University Press:  25 October 2004

PIERRE-ALAIN CHERIX ,
FLORIAN MARTIN  and
ALAIN VALETTE
PIERRE-ALAIN CHERIX
Affiliation:
Section de Mathématiques, Université de Genève, Rue du Lièvre 2-4, CP 240, CH-1211 Genève 24, Switzerland (e-mail: Pierre-Alain.Cherix@math.unige.ch)
FLORIAN MARTIN
Affiliation:
Institut de Mathématiques, Université de Neuchâtel, Rue Emile Argand 11, CH-2007 Neuchâtel, Switzerland (e-mail: florian.martin@unine.ch, alain.valette@unine.ch)
ALAIN VALETTE
Affiliation:
Institut de Mathématiques, Université de Neuchâtel, Rue Emile Argand 11, CH-2007 Neuchâtel, Switzerland (e-mail: florian.martin@unine.ch, alain.valette@unine.ch)
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce the notion of a space with measured walls, generalizing the concept of a space with walls due to Haglund and Paulin (Simplicité de groupes d'automorphismes d'espaces à courbure négative. Geom. Topol. Monograph1 (1998), 181–248). We observe that if a locally compact group G acts properly on a space with measured walls, then G has the Haagerup property. We conjecture that the converse holds and we prove this conjecture for the following classes of groups: discrete groups with the Haagerup property, closed subgroups of SO(n, 1), groups acting properly on real trees, SL2(K) where K is a global field and amenable groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 6 , December 2004 , pp. 1895 - 1908
Copyright
2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)