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Quantum invariants of Seifert 3–manifolds and their
asymptotic expansions
Soren Kold Hansen and Toshie Takata
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Geometry & Topology Monographs 4
(2002) 69–87
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Abstract
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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 J. E. Andersen.
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Keywords
quantum invariants, Seifert manifolds,
modular categories, quantum groups, asymptotic expansions
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Mathematical Subject Classification
Primary: 57M27
Secondary: 17B37, 18D10, 41A60
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Publication
Received: 3 December 2001
Accepted: 22 July 2002
Published: 19 September 2002
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