Quantum invariants of Seifert 3-manifolds and their asymptotic expansions

2002/10/01 by Soren Kold Hansen, Toshie Takata
Mathematics · #math.GT #math.QA #msc:57M27 #msc:17B37 #msc:18D10 #msc:41A60

paper · pdf

published as Geom. Topol. Monogr. 4 (2002) 69-87 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper6.abs.html

arxiv created 2002/10/01 · arxiv updated 2009/11/30

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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