4 problems

Let $M$ be a Riemannian $4k$-manifold with positive Ricci curvature that admits a string structure, meaning that the classifying map of its tangent bundle lifts from…

Let $M$ be a compact spin manifold with positive Ricci curvature and vanishing first Pontryagin class … The Hoehn–Stolz conjecture. The Witten genus of $M$ vanishes: … Here $D^L$ i…

Let $M$ be a highly connected manifold of dimension $n>8$. The Stolz–Höhn conjecture. If $M$ admits a metric with positive Ricci curvature, then its Witten genus vanishes. The Witt…

Let $X$ be a String manifold, so that its loop-space bundle admits a lift of its structure group from $\mathcal{L}\mathrm{Spin}_n$ to its universal central extension. Consider a hy…