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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)
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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

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