Quantum invariants of Seifert 3-manifolds and their asymptotic expansions

Soren Kold Hansen; Toshie Takata

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arXiv · math/0210011

Quantum invariants of Seifert 3-manifolds and their asymptotic expansions

Soren Kold Hansen·Toshie Takata

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Abstract

We report on recent results of the authors concerning calculations of quantum invariants of Seifert 3-manifolds. These results include a derivation of the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated with an arbitrary complex finite dimensional simple Lie algebra, and a determination of the asymptotic expansions of these invariants for lens spaces. Our results are in agreement with the asymptotic expansion conjecture due to JE Andersen [The Witten invariant of finite order mapping tori I, to appear in J. Reine Angew. Math.] and [The asymptotic expansion conjecture, from `Problems on invariants of knots and 3--manifolds', edited by T. Ohtsuki, http://www.ms.u-tokyo.ac.jp/~tomotada/proj01/].

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BibTeX RIS

Soren Kold Hansen, Toshie Takata. 2002-10-01. Quantum invariants of Seifert 3-manifolds and their asymptotic expansions. https://arxiv.org/abs/math/0210011

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