Twisted Alexander polynomials and character varieties of 2-bridge knot groups

Understand

We study the twisted Alexander polynomial from the viewpoint of the SL(2,C)-character variety of nonabelian representations of a knot group.

• It is known that if a knot is fibered, then the twisted Alexander polynomials associated with nonabelian SL(2,C)-representations are all monic.
• In this paper, we show that the converse holds for 2-bridge knots.
• Furthermore we show that for a 2-bridge knot there exists a curve component in the SL(2,C)-character variety such that if the knot is not fibered then there are only finitely many characters in the component for which the associated twisted Alexander polynomials are monic.