Title: On the minimal order of knots and the twisted Alexander polynomial

The twisted Alexander polynomial is defined as a generalization of the classical Alexander polynomial by Lin and Wada independently. We define the minimal order of a knot to be the order of the smallest finite group, so that the corresponding twisted Alexander polynomial is zero. In this talk, we consider some examples and properties of this minimal order. Moreover, we provide some formulas of the twisted Alexander polynomials.

 

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