2-BRIDGE NUMBERS OF TORUS KNOTS

Abstract

The 2-bridge number of knots was introduced by Hass, Rubinstein and Thompson [Knots and k-width, Geom. Dedicata143 (2009) 7–18] as a natural generalization of the bridge number introduced by Schubert [Über eine numerisch knoteninvariante, Math. Z.61 (1954) 245–288]. We show that the 2-bridge number of a torus knot of type (p, q) is (p - 1)q + 2 if 1 < p < q.