{"paper":{"title":"On the Witten--Reshetikhin--Turaev invariants of torus bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"J{\\o}rgen Ellegaard Andersen, S{\\o}ren Fuglede J{\\o}rgensen","submitted_at":"2012-06-12T14:50:49Z","abstract_excerpt":"By methods similar to those used by Lisa Jeffrey, we compute the quantum $\\mathrm{SU}(N)$-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 $\\mathrm{SU}(2)$ 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 result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2552","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}