Milnor conjecture (knot theory)

In knot theory, the Milnor conjecture says that the slice genus of the $$(p, q)$$ torus knot is


 * $$(p-1)(q-1)/2.$$

It is in a similar vein to the Thom conjecture.

It was first proved by gauge theoretic methods by Peter Kronheimer and Tomasz Mrowka. Jacob Rasmussen later gave a purely combinatorial proof using Khovanov homology, by means of the s-invariant.