8 problems

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 $M$ satisfy the assumptions of Theorem or Theorem; namely, in the first case, $M$ is a connected, oriented, closed manifold of even dimension with a semi-free $S^1$-action whos…

Consider reduced spin graphs of rank $2$, together with their systems of invariants and the induced notion of $k$-equivalence. The preceding result shows that, for fixed nonzero in…

Unstable relative Gromov–Lawson–Rosenberg conjecture. If the relative higher index of $D$ is zero in

Gromov's compactness conjecture. If the $\sideset{}{^1}\varprojlim$ higher index of the Dirac operator of $X$ vanishes, then $X$ admits a complete Riemannian metric with scalar cur…

Let $M$ be a closed spin $6$-manifold. Yau's conjecture. Every such $M$ admits a complex structure. This predicts that the topological spin condition in dimension six is sufficient…

Let $M$ be a compact oriented manifold whose universal covering does not admit a spin structure. Write $\Gamma=\pi_1(M)$, let $n=\dim M\ge 5$, and let … be the composition of the c…

The $11/8$-conjecture. This constraint is satisfied automatically for every such $M$; consequently, the list of spin homeotypes consisting of connected sums…