Amenable groups and Hadamard spaces with a totally disconnected isometry group
(2009) Commentarii Mathematici Helvetici — Vol. 84, n° 2, p. 437-455 (2009)
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- Abstract
- 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 partial derivative X-fine(infinity) which is a refinement of the visual boundary partial derivative(infinity) X. For each x is an element of partial derivative X-fine(infinity), the stabilizer G(x) is amenable.
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Caprace, P.-E. (2009). Amenable groups and Hadamard spaces with a totally disconnected isometry group. Commentarii Mathematici Helvetici, 84(2), 437-455. https://doi.org/10.4171/CMH/168 (Original work published 2009)