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

DOI10.4171/QT/175zbMath1531.57006arXiv2011.05484MaRDI QIDQ6353478

Publication date: 10 November 2020

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.

Mathematics Subject Classification ID

Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Knot theory (57K10) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

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