In knot theory, the Milnor conjecture says that the slice genus of the
(p,q)
(p-1)(q-1)/2.
It is in a similar vein to the Thom conjecture.
It was first proved by gauge theoretic methods by Peter Kronheimer and Tomasz Mrowka.[1] Jacob Rasmussen later gave a purely combinatorial proof using Khovanov homology, by means of the s-invariant.[2]