ADJOINT TWISTED ALEXANDER POLYNOMIALS FOR PARABOLIC REPRESENTATIONS OF GENUS ONE TWO-BRIDGE KNOTS
Abstract
In previous papers [19, 17], we computed the twisted Alexander polynomials and adjoint twisted Alexander polynomials for nonabelian SL2(C)-representations of genus one two-bridge knots. In this paper, we investigate their properties. When the SL2(C)-representation of a genus one two-bridge knot is parabolic, we show that (1) the coefficient of the highest degree term of the adjoint twisted Alexander polynomial is a rational multiple, independent of the representation, of the square of the twisted Alexander polynomial at t=1, and (2) the adjoint twisted Alexander polynomial is a monic polynomial if and only if the knot is fibered.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Kodai Mathematical Journal
- Volume
- 49
- Issue
- 1
- Pages
- 51–62
- Publication date
- 2 March 2026
- Language
- EN