3 problems

Let a very exotic sphere mean a homotopy sphere that does not bound a parallelizable manifold. The preceding results show that very exotic spheres exist in at least $99$ congruence…

Let $M$ be a highly connected manifold admitting a positive scalar curvature metric and with vanishing Witten genus. A homotopy-sphere Ricci-positivity conjecture. There exists a h…

An exotic sphere is a smooth manifold homeomorphic but not diffeomorphic to a standard sphere. A Riemannian metric is strictly $1/4$-pinched in the global sense when its sectional…