Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions
By S. K. Hansen, Toshie Takata. 2002
47 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fb07edbefd2ea48b9922db8d536c9f3eec49d18d
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Matrix model as a mirror of Chern-Simons theory (2002, methodology): “The path integral with Wilson lines in representation labeled by αR, αR′ inserted parallel to the axis of the solid tori before the gluing with U are given by [16, 17]”
- Problems on invariants of knots and 3-manifolds (2004, background): “follows from the fact that these invariants have non-trivial asymptotic expansion in the limit of large quantum level; see [354], [168], and Section 7.”
- Non-Abelian localization for Chern-Simons theory (2005, background): “…Rozansky managed to recast the known formula for Z(k), which initially involves an unwieldy sum over the integrable representations of an SU (2) WZW model at level k, into a simple sum of contour integrals and residues which can be formally identified with the contributions from the flat…”