Algebraic and Geometric Topology 1 (2001), paper no. 32, pages 627-686.

Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula

Soren Kold Hansen

Abstract. We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and $3$--manifolds, de Gruyter Stud. Math. 18, Walter de Gruyter (1994)], and the invariants are expressed in terms of the S- and T-matrices of the modular category. In another direction we derive a rational surgery formula, which states how the RT-invariants behave under rational surgery along framed links in arbitrary closed oriented 3-manifolds with embedded colored ribbon graphs. The surgery formula is used to give another derivation of the RT-invariants of Seifert manifolds with orientable base.

Keywords. Quantum invariants, Seifert manifolds, surgery, framed links, modular categories, quantum groups

AMS subject classification. Primary: 57M27. Secondary: 17B37, 18D10, 57M25.

DOI: 10.2140/agt.2001.1.627

Submitted: 9 April 2001. (Revised: 28 August 2001.) Accepted: 5 September 2001. Published: 30 October 2001.

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Soren Kold Hansen
Institut de Recherche Mathematique Avancee, Universite Louis Pasteur - C.N.R.S.
7 rue Rene Descartes, 67084 Strasbourg, France

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