Milnor's Conjecture

The Unknotting Number for a Torus Knot $(p,q)$ is $(p-1)(q-1)/2$. This 40-year-old Conjecture was proved (Adams 1994) in Kronheimer and Mrowka (1993, 1995).

See also Torus Knot, Unknotting Number

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, p. 113, 1994.

Kronheimer, P. B. and Mrowka, T. S. ``Gauge Theory for Embedded Surfaces. I.'' Topology 32, 773-826, 1993.

Kronheimer, P. B. and Mrowka, T. S. ``Gauge Theory for Embedded Surfaces. II.'' Topology 34, 37-97, 1995.