The topological analogue of the Slice-Ribbon Conjecture

A knot $K$ is topologically slice if it bounds a topological slice disk $\Delta$ in $B^4$. It is topologically homotopy ribbon if it bounds such a disk for which the inclusion-induced map

$$\pi_1(M_K)\to\pi_1(B^4\setminus\nu(\Delta))$$

is surjective, where $M_K$ is the zero-surgery manifold of $K$. Topological homotopy-ribbon conjecture. Every topologically slice knot is topologically homotopy ribbon. Every ribbon knot is homotopy ribbon, but the stated topological converse remains open.