The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups

Federico Franceschini, Roberto Frigerio, Maria Beatrice Pozzetti, Alessandro Sisto

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a new seminorm on exact bounded cohomology, we use these combinatorial classes to show that, in degree 3, the zero norm subspace of the bounded cohomology of an acylindrically hyperbolic group is infinite dimensional. In an appendix we use the same techniques to give a cohomological proof of a lower bound, originally due to Brock, on the volume of the mapping torus of a cobounded pseudo-Anosov homeomorphism of a closed surface in terms of its Teichmüller translation distance.

Original languageEnglish
Pages (from-to)89-139
Number of pages51
JournalCommentarii Mathematici Helvetici
Volume94
Issue number1
Early online date5 Mar 2019
DOIs
Publication statusPublished - 2019

Keywords

  • Homological bicombing
  • Hyperbolic manifolds
  • Mapping torus
  • Pseudo-Anosov automorphism
  • Quasi-cocycles
  • Relatively hyperbolic group
  • Riemannian volume
  • Simplicial volume

ASJC Scopus subject areas

  • Mathematics(all)

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