3 problems

Let $n-m\geq 3$. Write $\mathrm{V}^{pl}_{n,m}=\mathrm{PL}_n/\mathrm{PL}_{n,m}$ for the PL Stiefel space, and let $\mathrm{Operad}^h(E_m,E_n)$ be the derived mapping space of the li…

Smoothing conjecture. Every such $N$ is smoothable. More precisely, $N$ admits a transverse field of 2-planes and therefore there is an arbitrarily small topological isotopy carryi…

Let $M\to B$ and $M'\to B$ be tangentially homeomorphic smooth manifold bundles with common fiber a closed oriented even-dimensional manifold, and let $\Theta(M',M)$ denote their s…