Isometry groups of proper CAT(0)-spaces

Details Isometry groups of proper CAT(0)-spaces Isometry groups of proper CAT(0)-spaces

2008-10-21

arxiv.org/abs/0810.3755v2

Mathematics

Group Theory

writing improved, some details added, 33 pages

Scientific paper

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.

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