Difference between revisions of "Milnor unknotting conjecture"
From Encyclopedia of Mathematics
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''Kronheimer–Mrówka theorem'' | ''Kronheimer–Mrówka theorem'' | ||
| − | The unknotting number of the [[Torus knot|torus knot]] of type | + | The unknotting number of the [[Torus knot|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 [[#References|[a1]]] and generalized to positive links (cf. also [[Positive link|Positive link]]). | The conjecture was proven by P.B. Kronheimer and T.S. Mrówka [[#References|[a1]]] and generalized to positive links (cf. also [[Positive link|Positive link]]). | ||
Latest revision as of 14:20, 14 August 2014
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
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