A polynomial defined by the $SL(2;\mathbb{C})$-Reidemeister torsion for a homology 3-sphere obtained by Dehn-surgery along a torus knot

Abstract

Let $M_n$ be a homology 3-sphere obtained by $\frac{1}{n}$-Dehn surgery along a $(p,q)$-torus knot. We consider a polynomial ${\sigma }_{(p,q,n)}(t)$ whose zeros are the inverses of the Reideimeister torsion of $M_n$ for $SL(2;\mathbb{C})$-irreducible representations. We give an explicit formula of this polynomial by using Tchebychev polynomials of the first kind. Further we also give a 3-term relations of these polynomials.

References in corpus (3)

• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
• Reidemeister torsion of a 3-manifold obtained by a Dehn-surgery along the figure-eight knot
• A polynomial defined by the SL(2;C)-Reidemeister torsion for a homology 3-sphere obtained by a Dehn surgery along a (2p,q)-torus knot

Cited by in corpus (1)

• Some numerical computations on Reidemeister torsion for homology 3-spheres obtained by Dehn surgeries along the figure-eight knot