Commentarii Mathematici Helvetici


Full-Text PDF (176 KB) | Table of Contents | CMH summary
Volume 84, Issue 2, 2009, pp. 437–455
DOI: 10.4171/CMH/168

Amenable groups and Hadamard spaces with a totally disconnected isometry group

Pierre-Emmanuel Caprace[1]

(1) Département de Mathématiques, IRMP, Université Catholique de Louvain, Chemin du Cyclotron, 2, 1348, LOUVAIN-LA-NEUVE, BELGIUM

Let X be a locally compact Hadamard space and G be a totally disconnected group acting continuously, properly and cocompactly on X. We show that a closed subgroup of G is amenable if and only if it is (topologically locally finite)-by-(virtually abelian). We are led to consider a set fine  X which is a refinement of the visual boundary ∂X. For each xfine  X, the stabilizer Gx is amenable.

Keywords: Amenable group, CAT(0) space, totally disconnected group, locally finite group

Caprace Pierre-Emmanuel: Amenable groups and Hadamard spaces with a totally disconnected isometry group. Comment. Math. Helv. 84 (2009), 437-455. doi: 10.4171/CMH/168