JournalsggdVol. 6 , No. 3pp. 579–618

Isometry groups of proper CAT(0)-spaces of rank one

  • Ursula Hamenstädt

    Universität Bonn, Germany
Isometry groups of proper CAT(0)-spaces of rank one cover
Download PDF

Abstract

Let XX be a proper CAT(0)-space and let GG be a closed subgroup of the isometry group Iso(X)\mathrm{Iso}(X) of XX. We show that if GG is non-elementary and contains a rank-one element then its second continuous bounded cohomology group with coefficients in the regular representation is non-trivial. As a consequence, up to passing to an open subgroup of finite index, either GG is a compact extension of a totally disconnected group or GG is a compact extension of a simple Lie group of rank one.

Cite this article

Ursula Hamenstädt, Isometry groups of proper CAT(0)-spaces of rank one. Groups Geom. Dyn. 6 (2012), no. 3 pp. 579–618

DOI 10.4171/GGD/166