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.

69 pages, 13 figures

References in corpus (2)

• All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
• Gromov norm and Turaev-Viro invariants of 3-manifolds