Open AccessAmenable groups and Hadamard spaces with a totally disconnected isometry group
Author(s) -
Pierre–Emmanuel Caprace
Publication year - 2009
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.4171/cmh/168
Subject(s) - mathematics , isometry (riemannian geometry) , abelian group , locally compact space , combinatorics , group (periodic table) , boundary (topology) , hadamard transform , pure mathematics , mathematical analysis , physics , quantum mechanics
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