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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Reshetikhin–Turaev invariants of Seifert 3–manifolds and a rational surgery formula

Søren Kold Hansen

Algebraic & Geometric Topology 1 (2001) 627–686

arXiv: math.GT/0111057

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
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 17B37, 18D10, 57M25
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Publication
Received: 9 April 2001
Revised: 28 August 2001
Accepted: 5 September 2001
Published: 30 October 2001
Authors
Søren Kold Hansen
Institut de Recherche Mathématique Avancée
Université Louis Pasteur - C.N.R.S.
7 rue René Descartes
67084 Strasbourg
France