Mixing, malnormal subgroups and cohomology in degree one

  • Antoine Gournay

    Technische Universität Dresden, Germany


The aim of the current paper is to explore the implications on the group of the non-vanishing of the cohomology in degree one of one of its representation , given some mixing conditions on . 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 , will either be “small,” almost-malnormal or 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 -cohomology in degree one are obtained as an intermediate step.

Cite this article

Antoine Gournay, Mixing, malnormal subgroups and cohomology in degree one. Groups Geom. Dyn. 12 (2018), no. 4, pp. 1371–1416

DOI 10.4171/GGD/472