4 problems

Nonexistence conjecture. There is no $\mathbf{E}_7$-structure on $S^{133}$.

Let $M^{\prime}_{k,l}$ be the total space of the corresponding $S^3$-bundle over $\mathbb{C}P^2$, with Euler-class parameter $l$. It is known that … when $l$ is even. Escher's conj…

Frigerio's conjecture. The Euler class of every topologically flat sphere bundle admits a bounded representative.

Let $\pi\colon E\to M$ be a topologically flat sphere bundle, meaning a sphere bundle whose structure group reduces to the homeomorphism group of the sphere. Let ${\mathrm{eu}}(E)$…