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

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.