Amenable groups and Hadamard spaces with a totally disconnected isometry group

Details Amenable groups and Hadamard spaces with a totally disconnected isometry group Amenable groups and Hadamard spaces with a totally disconnected isometry group

2007-05-14

arxiv.org/abs/0705.1980v1

Mathematics

Group Theory

15 pages

Scientific paper

10.4171/MCH/168

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 $\bdfine X$ which is a refinement of the visual boundary $\bd X$. For each $x \in \bdfine X$, the stabilizer $G_x$ is amenable.

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