Representations of Knot Groups and Twisted Alexander Polynomials

We present a twisted version of the Alexander polynomial associated with a matrix rep- resentation of the knot group.Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.

纽结理论中的Alexander多项式

本文阐述了Alexander多项式关于纽结与其全体状态之内积的表达式,证明了纽结余部赋以模结构而给出的表示矩阵的行列式即为Alexander多项式,并给出由自由群环上的自由导数求出Alexander多项式的方法。