Höhn–Stolz conjecture for the Witten genus

Let $M$ be a closed string manifold. The Höhn–Stolz conjecture. If $M$ admits a Riemannian metric of positive Ricci curvature, then the Witten genus $W(M)$ vanishes.

The conjecture relates positive Ricci curvature on string manifolds to vanishing of the Witten genus, an integral modular form associated with a closed string manifold. The source discusses its connection with vanishing chiral algebras in two-dimensional sigma models; its resolution status is not specified here.