针对环面链环的辫子数的性质进行研究与分析。辫子数是一种重要的纽结不变量,Morton-Franks-Williams不等式HOMFLY多项式的形式给出了对链环的辫子数的下界估计,Yamada则以Seifert圈数的形式给出了上界的限制。利用Morton-Franks-Williams不等式,给出(m,n)-环面链环的辫子数是min(m,n).
The braid index of torus links, which is an important invariant in knot theory, is studied. Morton - Franks - Williams inequality gives the lower bound for the braid index in terms of the HOMFLY polynomial, while Yamada gives the upper bound in terms of Seifert circles. By using the Morton - Franks - Williams inequality, it is shown that for the ( m, n) - torus link L, the braid index of L is min (m,n).