环面链环的辫子数

摘要

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 HOMFLYpolynomial, 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) - toms link L, the braid index of L is min(m,n).