2 problems

Universal cork conjecture. There is no universal cork, i.e. no cork $(U,f_U)$ relating every exotic pair of simply-connected, closed $4$-manifolds.

Let $C=C(r,s;m)$ be Gompf's cork, and define the twisted double … Here $r,s,m$ are integers with $r,s>0>m$, and $k$ is a nonzero integer. Gompf's conjecture. The homotopy 4-sphere…