An estimate for the unknotting numbers of torus knots

Abstract

In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2, q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2, q), (3,4) and (3,5), this has already been known.