The superpotential conjecture for fundamental group algebras of acyclic manifolds

Let $M$ be an acyclic oriented compact manifold of dimension $d$, and let $k[\pi_1(M)]$ denote its fundamental group algebra. Superpotential conjecture. If $M$ is an acyclic oriented compact manifold of dimension $d$, then $k[\pi_1(M)]$ is a superpotential algebra. The paper presents counterexamples to this conjecture, so the claim is refuted in the stated generality.