Weakly bounded cohomology classes and a counterexample to a conjecture of Gromov

TL;DR

This paper constructs a finitely presented group with a specific cohomology class to disprove Gromov's conjecture on bounded primitives of differential forms on universal covers.

Contribution

It introduces a counterexample to Gromov's conjecture by exhibiting a group with a weakly bounded but not bounded cohomology class.

Findings

Counterexample to Gromov's conjecture established

Existence of a finitely presented group with a weakly bounded cohomology class

Disproof of the long-standing conjecture in geometric topology

Abstract

We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds.