Geodesic
Isometry groups of proper CAT(0)-spaces of rank one
Ursula Hamenstädt1 orcid
1Universität Bonn, Germany
Groups, geometry, and dynamics, Tome 6 (2012) no. 3, pp. 579-618

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DOI

Let X be a proper CAT(0)-space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G 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 G is a compact extension of a totally disconnected group or G is a compact extension of a simple Lie group of rank one.
DOI : 10.4171/ggd/166
Classification : 20-XX, 00-XX
Mots-clés : Bounded cohomology, isometry groups, CAT(0)-spaces, rigidity

Ursula Hamenstädt  1

1 Universität Bonn, Germany 
Ursula Hamenstädt. Isometry groups of proper CAT(0)-spaces of rank one. Groups, geometry, and dynamics, Tome 6 (2012) no. 3, pp. 579-618. doi: 10.4171/ggd/166
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     title = {Isometry groups of proper {CAT(0)-spaces} of rank one},
     journal = {Groups, geometry, and dynamics},
     pages = {579--618},
     year = {2012},
     volume = {6},
     number = {3},
     doi = {10.4171/ggd/166},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/166/}
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