Resolve the Stolz conjecture for positive Ricci curvature

Prove or disprove that the Witten genus vanishes on every string manifold admitting a metric of everywhere positive Ricci curvature.

Background

The thesis relates the Witten genus w ⁣:π∗MO⟨8⟩→tmfw\colon \pi_*MO\langle 8\rangle\to tmf to geometric curvature conditions on string manifolds. It identifies the asserted vanishing under everywhere positive Ricci curvature as the Stolz conjecture, thereby recording an explicitly unresolved conjecture relevant to the geometric interpretation of string bordism and the tmftmf-orientation.

References

Analogously, the Witten genus $w: \pi_{*} MO \langle 8 \rangle \rightarrow tmf$ is conjectured to vanish on string manifolds that admit a metric of everywhere positive Ricci curvature.

— On the cobordism groups of $O\langle n\rangle$-manifolds  (2609.28804 - Abdallah, 23 Sep 2026) in Section 1, Introduction, discussion of orientation maps and geometric applications