The twisted Reidemeister torsion of an iterated torus knot

TL;DR

This paper computes the twisted Reidemeister torsion for iterated torus knots and links it to the asymptotic behavior of the colored Jones polynomial, revealing new insights into knot invariants.

Contribution

It introduces a method to calculate the twisted Reidemeister torsion for iterated torus knots and connects it to quantum invariants like the colored Jones polynomial.

Findings

Twisted Reidemeister torsion is explicitly computed for iterated torus knots.

The torsion appears in the asymptotic expansion of the colored Jones polynomial.

The work bridges classical topological invariants with quantum knot invariants.

Abstract

We calculate the twisted Reidemeister torsion of the complement of an iterated torus knot associated with a representation of its fundamental group to the complex special linear group of degree two. We also show that the twisted Reidemeister torsions associated with various representations appear in the asymptotic expansion of the colored Jones polynomial.