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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) by Kronheimer and Mrowka (1993, 1995).

See also

Torus Knot, Unknotting Number

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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.

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Milnor's Conjecture

Cite this as:

Weisstein, Eric W. "Milnor's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MilnorsConjecture.html

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