Quantum Topology

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Volume 3, Issue 3/4, 2012, pp. 377–421
DOI: 10.4171/QT/33

Published online: 2012-05-30

The Witten-Reshetikhin-Turaev invariants of finite order mapping tori II

Jørgen Ellegaard Andersen[1] and Benjamin Himpel[2]

(1) University of Aarhus, Denmark
(2) University of Aarhus, Denmark

We identify the leading order term of the asymptotic expansion of the Witten–Reshetikhin–Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-connected compact Lie groups. The square root of the Reidemeister torsion is used as a density on the moduli space of flat connections and the leading order term is identified with the integral over this moduli space of this density weighted by a certain phase for each component of the moduli space. We also identify this phase in terms of classical invariants such as Chern–Simons invariants, eta invariants, spectral flow and the $\rho$-invariant. As a result, we show agreement with the semiclassical approximation as predicted by the method of stationary phase.

Keywords: Witten–Reshetikhin–Turaev quantum invariant, asymptotics, semiclassical approximation, Reidemeister torsion, $\rho$-invariant, eta invariant, spectral flow

Andersen Jørgen Ellegaard, Himpel Benjamin: The Witten-Reshetikhin-Turaev invariants of finite order mapping tori II. Quantum Topol. 3 (2012), 377-421. doi: 10.4171/QT/33