Trivial cup products in bounded cohomology of the free group via aligned chains

TL;DR

This paper demonstrates that certain types of quasimorphisms in the bounded cohomology of free groups have trivial cup products with any bounded cohomology class of positive degree, simplifying the algebraic structure.

Contribution

It establishes the triviality of cup products involving specific quasimorphisms in bounded cohomology of free groups, providing new insights into their algebraic properties.

Findings

Cup products of $ riangle$-decomposable quasimorphisms with any bounded cohomology class are trivial.

Brooks and Rolli quasimorphisms also have trivial cup products with arbitrary positive degree classes.

Results simplify understanding of the algebraic structure in bounded cohomology of free groups.

Abstract

We prove that the cup product of $\Delta$-decomposable quasimorphisms, Brooks quasimorphisms or Rolli quasimorphisms with any bounded cohomology class of arbitrary positive degree is trivial.