Refine search
Actions for selected content:
1 results
Fibering of double twist knots via the adjoint hyperbolic torsion polynomial
- Part of
-
- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 03 August 2026, pp. 1-15
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
For a hyperbolic knot $K$
in $S^3$
, the adjoint hyperbolic torsion polynomial $\mathcal T^{\mathrm {Ad}}_K(t) \in \mathbb C[t^{\pm 1}]$
is defined as a normalization of the twisted Alexander polynomial of $K$
associated with the $\mathrm {SL}_3(\mathbb C)$
-representation obtained by composing the holonomy representation of $K$
with the adjoint action of $\mathrm {SL}_2(\mathbb C)$
on its Lie algebra $\mathfrak {sl}_2(\mathbb C)$
. In this article, we consider the adjoint hyperbolic torsion polynomial for a two-parameter family of rational knots called double twist knots and show that $\mathcal T^{\mathrm {Ad}}_K(t)$
determines the genus and fibering of this family by using algebraic integers.
