Isometry groups of proper CAT(0)-spaces

Abstract

Let G be a closed subgroup of the isometry group of a proper CAT(0)-space X. We show that if G is non-elementary and contains a rank-one element then its second 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 G is a compact extension of a totally disconnected group or G is a compact extension of a simple Lie group of rank one.

writing improved, some details added, 33 pages

References in corpus (5)

• Bounded cohomology of subgroups of mapping class groups
• Isometry groups of non-positively curved spaces: structure theory
• Rank-one isometries of proper CAT(0)-spaces
• A characterization of higher rank symmetric spaces via bounded cohomology
• Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups

Cited by in corpus (5)

• Induced quasi-cocycles on groups with hyperbolically embedded subgroups
• The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes
• Lines of minima in Outer space
• Rank-one isometries of proper CAT(0)-spaces
• Bounded cohomology with coefficients in uniformly convex Banach spaces