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Quantum invariants of Seifert 3–manifolds and their asymptotic expansions

Soren Kold Hansen and Toshie Takata

Geometry & Topology Monographs 4 (2002) 69–87

DOI: 10.2140/gtm.2002.4.69

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 J. E. Andersen.

Keywords

quantum invariants, Seifert manifolds, modular categories, quantum groups, asymptotic expansions

Mathematical Subject Classification

Primary: 57M27

Secondary: 17B37, 18D10, 41A60

References
Publication

Received: 3 December 2001
Accepted: 22 July 2002
Published: 19 September 2002

Authors
Soren Kold Hansen
School of Mathematics
University of Edinburgh
JCMB
King's Buildings
Edinburgh EH9 3JZ
UK
Toshie Takata
Department of Mathematics
Faculty of Science
Niigata University
Niigata 950-2181
Japan