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RESHETIKHIN–TURAEV INVARIANTS OF SEIFERT 3-MANIFOLDS FOR CLASSICAL SIMPLE LIE ALGEBRAS

SØREN KOLD HANSEN

Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany

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and

TOSHIE TAKATA

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

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https://doi.org/10.1142/S0218216504003342Cited by:18 (Source: Crossref)

Abstract

We derive explicit formulas for the Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra in terms of the Seifert invariants and standard data for . A main corollary is a determination of the full asymptotic expansions of these invariants for lens spaces in the limit of large quantum level. This result is in agreement with the asymptotic expansion conjecture due to Andersen [1,2].

Keywords:

AMSC: Primary 57M27, Secondary 17B37, Secondary 18D10, Secondary 41A60

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