On the Witten--Reshetikhin--Turaev invariants of torus bundles

2012/06/12 by Jørgen Ellegaard Andersen, Søren Fuglede Jørgensen, Andersen, Jørgen Ellegaard +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1206.2552

openalex publication_date 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By methods similar to those used by Lisa Jeffrey, we compute the quantum SU(N)-invariants for mapping tori of trace 2 homeomorphisms of a genus 1 surface when N = 2,3 and discuss their asymptotics. In particular, we obtain directly a proof of a version of Witten's asymptotic expansion conjecture for these 3-manifolds. We further prove the growth rate conjecture for these 3-manifolds in the SU(2) case, where we also allow the 3-manifolds to contain certain knots. In this case we also discuss trace -2 homeomorphisms, obtaining -- in combination with Jeffrey's results -- a proof of the asymptotic expansion conjecture for all torus bundles.

Citations

• Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory

Related

• The Witten-Reshetikhin-Turaev invariants of finite order mapping tori I
• Quantum invariants of Seifert 3-manifolds and their asymptotic expansions
• Analytic asymptotic expansions of the Reshetikhin--Turaev invariants of Seifert 3-manifolds for SU(2)
• Classical and Quantum Algorithms for Topological Invariants of Torus Bundles
• Asymptotics of quantum representations of surface groups