Bounded cohomology and virtually free hyperbolically embedded subgroups

Tobias Hartnick, Alessandro Sisto

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Using a probabilistic argument we show that the second bounded cohomology of a finitely-generated acylindrically hyperbolic group G (e.g., a non-elementary hyperbolic or relatively hyperbolic group, non-exceptional mapping class group, Out.Fn/, . . .) 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 G is a (non-free) hyperbolic group. The corresponding statement fails in general for the third bounded cohomology, even for surface groups.

Original languageEnglish
Pages (from-to)677-694
Number of pages18
JournalGroups, Geometry, and Dynamics
Volume13
Issue number2
Early online date6 May 2019
DOIs
Publication statusPublished - 2019

Keywords

  • Acylindrically hyperbolic
  • Bounded cohomology
  • Hyperbolically embedded
  • Quasimorphisms
  • Random walks

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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