Amenable groups and Hadamard spaces with a totally disconnected isometry group

  • Pierre-Emmanuel Caprace

    Université Catholique de Louvain, Belgium

Abstract

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

Cite this article

Pierre-Emmanuel Caprace, Amenable groups and Hadamard spaces with a totally disconnected isometry group. Comment. Math. Helv. 84 (2009), no. 2, pp. 437–455

DOI 10.4171/CMH/168