Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 6, pages 69--87.

Quantum invariants of Seifert 3-manifolds and their asymptotic expansions

Soren Kold Hansen Toshie Takata

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,].

Keywords. Quantum invariants, Seifert manifolds, modular categories, quantum groups, asymptotic expansions

AMS subject classification. Primary: 57M27. Secondary: 17B37, 18D10, 41A60.

E-print: arXiv:math.GT/0210011

Submitted to GT on 3 December 2001. Paper accepted 22 July 2002. Paper published 19 September 2002.

Notes on file formats

Soren Kold Hansen Toshie Takata
Dept of Maths and Stats, University of Edinburgh, JCMB
King's Buildings, Edinburgh EH9 3JZ, UK

Department of Mathematics, Faculty of Science
Niigata University, Niigata 950-2181, Japan


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