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Source: Milnor conjecture (knot theory)

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

(
p
,
q
)

{\displaystyle (p,q)}

torus knot is

(
p
−
1
)
(
q
−
1
)

/

2.

{\displaystyle (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.