In knot theory, the Milnor conjecture says that the slice genus of the
torus knot is 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.
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