Representations of knot groups and twisted Alexander polynomials (Q5946536)

The author considers knots in the 3-sphere and presents a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. The classical Alexander polynomial is the one associated with 1-dimensional representations. Examples of knots with the same classical Alexander polynomial but different twisted Alexander polynomials are given. This article appeared first in 1990 as a Columbia University preprint. Since then further works on the same topic have been published by several authors. See for example [\textit{P. Kirk} and \textit{C. Livingston}, Topology 38, No. 3, 635-661 (1999; Zbl 0928.57005)].