Milnor conjecture (knot theory)

Template:Short description Template:Otheruses 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.

References

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