Bounded cohomology with coefficients in uniformly convex Banach spaces

  • Mladen Bestvina

    University of Utah, Salt Lake City, USA
  • Kenneth Bromberg

    University of Utah, Salt Lake City, USA
  • Koji Fujiwara

    Kyoto University, Japan

Abstract

We show that for acylindrically hyperbolic groups (with no nontrivial finite normal subgroups) and arbitrary unitary representation of in a (nonzero) uniformly convex Banach space the vector space is infinite dimensional. The result was known for the regular representations on with by a different argument. But our result is new even for a non-abelian free group in this great generality for representations, and also the case for acylindrically hyperbolic groups follows as an application.

Cite this article

Mladen Bestvina, Kenneth Bromberg, Koji Fujiwara, Bounded cohomology with coefficients in uniformly convex Banach spaces. Comment. Math. Helv. 91 (2016), no. 2, pp. 203–218

DOI 10.4171/CMH/383