For a Braid with strands, components, positive crossings, and negative crossings,

where are the smallest number of positive and negative crossings which must be changed to crossings of the opposite sign. These inequalities imply Bennequin's Conjecture. Menasco's theorem can be extended to arbitrary knot diagrams.

**References**

Cipra, B. ``From Knot to Unknot.'' *What's Happening in the Mathematical Sciences, Vol. 2.*
Providence, RI: Amer. Math. Soc., pp. 8-13, 1994.

Menasco, W. W. ``The Bennequin-Milnor Unknotting Conjectures.'' *C. R. Acad. Sci. Paris Sér. I Math.* **318**, 831-836, 1994.

© 1996-9

1999-05-26