A braid with strands and components with positive crossings and negative crossings satisfies
where
is the unknotting number. While the second part
of the inequality was already known to be true (Boileau
and Weber, 1983, 1984) at the time the conjecture was proposed, the proof of the
entire conjecture was completed using results of Kronheimer and Mrowka on Milnor's
conjecture (and, independently, using the slice-Bennequin
inequality).
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strands and 
components with 
positive crossings and 
negative crossings satisfies
is the unknotting number. While the second part
of the inequality was already known to be true (Boileau
and Weber, 1983, 1984) at the time the conjecture was proposed, the proof of the
entire conjecture was completed using results of Kronheimer and Mrowka on Milnor's
conjecture (and, independently, using the slice-Bennequin
inequality).
