The Gluck ball 5-ball conjecture

A Gluck ball is the Poincare 4-ball associated with a Gluck-twisted $S^4$. Gluck ball 5-ball conjecture. If $\Delta^4$ is a Gluck ball, then

$$\Delta^4\times I\cong B^5.$$

This is described as a special case of the Gluck conjecture, which asks whether a Gluck-twisted $S^4$ is diffeomorphic to $S^4$, and remains open.