Fibering of double twist knots via the adjoint hyperbolic torsion polynomial

For a hyperbolic knot in 3 , the adjoint hyperbolic torsion polynomial T Ad ( ) ∈ C[ ±1 ] is defined as a normalization of the twisted Alexander polynomial of associated with the SL 3 (C)representation obtained by composing the holonomy representation of with the adjoint action of SL 2 (C) on its Lie algebra 2 (C).In this paper we consider the adjoint hyperbolic torsion polynomial for a two-parameter family of rational knots called double twist knots, and show that T Ad ( ) determines the genus and fibering of this family by using algebraic integers.