A vanishing criterion for cup products and Massey products in bounded cohomology

TL;DR

This paper establishes a general criterion for when products in bounded cohomology vanish, enabling new proofs and extensions of results related to cup and Massey products in various group cohomology contexts.

Contribution

It introduces a uniform vanishing criterion for products in bounded cohomology, extending previous results for free groups and group actions on CAT(0) cube complexes.

Findings

Reproved known vanishing results for cup products in bounded cohomology.

Extended vanishing results to Massey triple products.

Provided a unified approach applicable to different group actions.

Abstract

We give a uniform vanishing criterion for products in bounded cohomology. This allows us to reprove and extend previous vanishing results for cup products and Massey triple products in the bounded cohomology of free groups and in the equivariant bounded cohomology of group actions on CAT(0) cube complexes.