Milnor unknotting conjecture

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Kronheimer–Mrówka theorem

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


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.


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