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

Ursula Hamenstädt | Zendy

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

Author(s) -

Ursula Hamenstädt

Publication year - 2012

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/166

Subject(s) - mathematics , rank (graph theory) , isometry (riemannian geometry) , pure mathematics , combinatorics

LetX be a proper CAT.0/-space and letG 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. Mathematics Subject Classification (2010). 20F67, 20J06.

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