Doubly sliced knots and doubled disk knots (Q791931)

It is shown that the cohomology ring of a doubly-sliced n-knot is hyperbolic, in a natural sense, and that this result implies the conditions already known in the middle dimensions. Then it is shown that the double of a disk knot is doubly-sliced, and for \(n=1,2\), examples are given of doubly-sliced n-knots which are not doubled disk knots. On the other hand, it is shown that for \(q\geq 2\), any simple doubly-sliced (2q- 1)-knot is the double of a disk knot.