JournalsggdVol. 13, No. 2pp. 677–694

Bounded cohomology and virtually free hyperbolically embedded subgroups

  • Tobias Hartnick

    Justus-Liebig Universität Giessen, Germany
  • Alessandro Sisto

    ETH Zürich, Switzerland
Bounded cohomology and virtually free hyperbolically embedded subgroups cover

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Abstract

Using a probabilistic argument we show that the second bounded cohomology of a finitely-generated acylindrically hyperbolic group GG (e.g., a non-elementary hyperbolic or relatively hyperbolic group, non-exceptional mapping class group, Out(Fn),)(F_n),…) embeds via the natural restriction maps into the inverse limit of the second bounded cohomologies of its virtually free subgroups, and in fact even into the inverse limit of the second bounded cohomologies of its hyperbolically embedded virtually free subgroups. This result is new and non-trivial even in the case where GG is a (non-free) hyperbolic group. The corresponding statement fails in general for the third bounded cohomology, even for surface groups.

Cite this article

Tobias Hartnick, Alessandro Sisto, Bounded cohomology and virtually free hyperbolically embedded subgroups. Groups Geom. Dyn. 13 (2019), no. 2, pp. 677–694

DOI 10.4171/GGD/500