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• W2475952652 abstract "The aim of the current paper is to explore the implications on the group $G$ of the non-vanishing of the cohomology in degree one of one of its representation $pi$, given some mixing conditions on $pi$. For example, harmonic cocycles of weakly mixing unitary representations factorise by the FC-centre. In that case non-vanishing implies the FC-centre is trivial or fixes a vector. Next, for any subgroup $H < G$, $H$ will either be “small,” almost-malnormal or $pi_{|H}$ also has non-trivial cohomology in degree one (in this statement, “small,” reduced vs unreduced cohomology and unitary vs generic depend on the mixing condition). The notion of q-normal subgroups is an important ingredient of the proof and results on the vanishing of the reduced $ell^p$-cohomology in degree one are obtained as an intermediate step." @default.
• W2475952652 created "2016-08-23" @default.
• W2475952652 creator A5032283666 @default.
• W2475952652 date "2018-11-01" @default.
• W2475952652 modified "2023-09-27" @default.
• W2475952652 title "Mixing, malnormal subgroups and cohomology in degree one" @default.
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• W2475952652 doi "https://doi.org/10.4171/ggd/472" @default.
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