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

الأصل · EN

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.