Ribbon Knots in S 4

Our main results are several new obstructions to knotted 2‐spheres' in S 4 being ribbon knots and the application of these to characterize fibered ribbon knots in S 4 . For knots which bound punctured S 1 × S 2 , all of the known ribbon invariants vanish. We produce a new obstruction which detects the first known non‐ribbon knots in this class. Finally, we show that ribbon knots are naturally associated with links whose groups are free, but not on their meridians.