Quantum invariants of three-manifolds obtained by surgeries along torus knots

TL;DR

This paper investigates the asymptotic behavior of quantum invariants of three-manifolds obtained via surgeries on torus knots, linking them to classical topological invariants like Chern-Simons invariants and Reidemeister torsions.

Contribution

It provides a detailed description of the asymptotics of Witten-Reshetikhin-Turaev invariants for Seifert fibered spaces derived from torus knot surgeries, connecting quantum and classical invariants.

Findings

Expresses quantum invariants as sums involving Chern-Simons invariants.

Links quantum invariants to twisted Reidemeister torsions.

Shows the asymptotic behavior relates to representations of the fundamental group.

Abstract

We study the asymptotic behavior of the Witten-Reshetikhin-Turaev invariant associated with the square of the $n$-th root of unity with odd $n$ for a Seifert fibered space obtained by an integral Dehn surgery along a torus knot. We show that it can be described as a sum of the Chern-Simons invariants and the twisted Reidemeister torsions both associated with representations of the fundamental group to the two-dimensional complex special linear group.