Geodesic
Mixing, malnormal subgroups and cohomology in degree one
Antoine Gournay1
1Technische Universität Dresden, Germany
Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1371-1416

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DOI

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 π, given some mixing conditions on π. 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 π∣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 lp-cohomology in degree one are obtained as an intermediate step.
DOI : 10.4171/ggd/472
Classification : 20-XX, 22-XX, 43-XX
Mots-clés : Mildly mixing, malnormal subgroups, cohomology of group representations, lp-cohomology, Liouville groups

Antoine Gournay  1

1 Technische Universität Dresden, Germany 
Antoine Gournay. Mixing, malnormal subgroups and cohomology in degree one. Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1371-1416. doi: 10.4171/ggd/472
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