3 problems

Let $p:M\to B$ and $p':M'\to B$ be smooth manifold bundles with closed even-dimensional fibers, with $M'$ an exotic smoothing of $M$, meaning that $M'$ is fiberwise tangentially ho…

Let $p:M\to B$ be a smooth manifold bundle with closed even-dimensional fibers, and consider stable exotic smoothings of such bundles after rationalization. Goette–Igusa's Rigidity…

Let $W$ be an arbitrary closed manifold on which $SU(2)$ acts smoothly and non-trivially. Let $s\colon BSU(2) \to B\operatorname{Diff}(W)$ be the induced map on classifying spaces,…