Commentarii Mathematici Helvetici
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Amenable groups and Hadamard spaces with a totally disconnected isometry groupPierre-Emmanuel Caprace (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 x ∈ ∂fine∞ 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