Let $S_1$, $S_2$ be homologous embedded 2-spheres in a compact smooth 4-manifold. Under which additional conditions are they smoothly isotopic? I am interested in the state of the art picture when $S_i$ are spheres with self-intersection $-2$ in a K3 surface. However, any related information (for other 4-manifolds, and for extra assumptions on $S_i$, such as Lagrangian or pseudoholomorphic) will be also much appreciated.
I looked around and found many papers about knotted 2-tori and Lagrangian 2-tori in symplectic 4-manifolds, but nothing about knotted 2-spheres.
