The Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori I

TL;DR

This paper proves conjectures about the asymptotic behavior of Witten-Reshetikhin-Turaev invariants for links in certain 3-manifolds, using geometric quantization and conformal field theory methods.

Contribution

It establishes the conjectures for natural links in mapping tori of finite-order surface automorphisms, connecting geometric quantization with quantum invariants.

Findings

Proved asymptotic expansion conjecture for specific links

Confirmed growth rate conjecture in the studied setting

Linked geometric quantization with conformal field theory construction

Abstract

We state Asymptotic Expansion and Growth Rate conjectures for the Witten-Reshetikhin-Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automorphisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten-Reshetikhin-Turaev invariants using conformal field theory, as was recently completed by Andersen and Ueno.