Trivial Massey Product in Bounded Cohomology

TL;DR

This paper demonstrates that certain Massey triple products in bounded cohomology are always trivial under specific conditions in free groups and negatively curved manifolds, revealing new structural insights.

Contribution

It establishes the triviality of Massey triple products in bounded cohomology for particular classes of groups and manifolds, highlighting conditions for triviality.

Findings

Massey triple product is trivial in bounded cohomology of free groups under specific conditions.

Massey triple product is trivial in bounded cohomology of negatively curved manifolds with exact forms.

Provides new understanding of the structure of bounded cohomology in these contexts.

Abstract

We show that in the bounded cohomology of non-abelian free groups the Massey triple product is always trivial when the second factor is represented by the coboundary of a decomposable quasi-morphism. We also show that in the bounded cohomology of a negatively curved compact Riemannian manifold the Massey triple product is always trivial when the second factor is represented by an exact differential form.