4 problems

Boundary-universal cork conjecture. There is no $\partial$-universal cork.

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…

Let $W$ be a cork, let $X$ be a symplectic $4$--manifold with $b_2^+(X)\geq 2$, and suppose that $W$ embeds symplectically in $X$. A fake copy is a manifold homeomorphic but not di…