Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions

Details Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions

2002-09-30

arxiv.org/abs/math/0209403v2

J. Knot Theory Ramifications 13 (2004), no. 5, 617--668

Mathematics

Geometric Topology

61 pages, 3 figures, comments added in the introduction, the bibliography changed slightly, minor changes in notation, some mi

Scientific paper

We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra $\mathfrak g$ in terms of the Seifert invariants and standard data for $\mathfrak g$. A main corollary is a determination of the full asymptotic expansions of these invariants for lens spaces in the limit of large quantum level. Our results are in agreement with the asymptotic expansion conjecture due to J. E. Andersen.

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