The circle-bundle superpotential conjecture for acyclic manifold group algebras

Let $M$ be an acyclic compact orientable manifold, let $\pi(M)$ denote its fundamental group, and let $k[\pi(M)]$ be the corresponding group algebra. Circle-bundle superpotential conjecture. If $M$ is a circle bundle, then $k[\pi(M)]$ is a superpotential algebra. This is introduced as a weaker conjecture after counterexamples to the broader claim; the supplied text gives no resolution of this circle-bundle case.