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

TL;DR

This paper connects the asymptotic behavior of Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants, providing a semiclassical interpretation through detailed geometric and topological analysis.

Contribution

It identifies the leading order term of the invariants' asymptotics with classical invariants for all simple, simply-connected compact Lie groups, extending previous results.

Findings

Leading order term expressed as an integral over the moduli space of flat connections.

Identification of phase factors with classical invariants such as Chern-Simons and eta invariants.

Confirmation of the semiclassical approximation via stationary phase method.

Abstract

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.