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Advances in Mathematics 197 (2005) 499522 www.elsevier.com/locate/aim

Summary: Advances in Mathematics 197 (2005) 499­522
Uniform non-amenability
G.N. Arzhantsevaa, J. Burillob, M. Lustigc, L. Reevesc,
H. Shortd,, E. Venturae
aUniversity of Geneva, CH-1211 Geneva 4, Switzerland
bUniversitat Politècnica de Catalunya, Avda. del Canal Olímpic, 08860 Castelldefels (Barcelona), Spain
cLATP, UMR CNRS 6632, Frumam, Université d'Aix-Marseille III, Avenue Escadrille Normandie-Niemen,
13397 Marseille 20, France
dLATP, UMR CNRS 6632, Frumam, University de Provence, CMI, 39 Rue Joliot Curie,
13453 Marseille 13, France
eUniversitat Politècnica de Catalunya, Av. Bases de Manresa 61 - 73, 08240 Manresa (Barcelona), Spain
Received 21 March 2003; accepted 26 October 2004
Communicated by Laszlo Lovasz
Available online 21 December 2004
For any finitely generated group G an invariant FZl G 0 is introduced which measures
the "amount of non-amenability" of G. If G is amenable, then FZl G = 0. If FZl G > 0, we
call G uniformly non-amenable. We study the basic properties of this invariant; for example,
its behaviour when passing to subgroups and quotients of G. We prove that the following


Source: Arzhantseva, Goulnara N. - Section de Mathématiques, Université de Genève


Collections: Mathematics