Amenable groups and Hadamard spaces with a totally disconnected isometry group | Zendy

PierreEmmanuel Caprace | Zendy

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Amenable groups and Hadamard spaces with a totally disconnected isometry group

Author(s) -

PierreEmmanuel 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) , locally compact space , hadamard transform , totally disconnected space , abelian group , group (periodic table) , boundary (topology) , isometry group , hausdorff space , combinatorics , pure mathematics , space (punctuation) , discrete mathematics , mathematical analysis , computer science , physics , quantum mechanics , operating system

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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