# Milnor unknotting conjecture

From Encyclopedia of Mathematics

*Kronheimer–Mrówka theorem*

The unknotting number of the torus knot of type $(p,q)$ is equal to

$$\frac{(p-1)(q-1)}{2}.$$

The conjecture was proven by P.B. Kronheimer and T.S. Mrówka [a1] and generalized to positive links (cf. also Positive link).

See also Link.

#### References

[a1] | P.B. Kronheimer, T.S. Mrowka, "Gauge theory for embedded surfaces I" Topology , 32 : 4 (1993) pp. 773–826 |

**How to Cite This Entry:**

Milnor unknotting conjecture.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Milnor_unknotting_conjecture&oldid=32915

This article was adapted from an original article by Jozef Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article