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Abstract
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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
– and
–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.
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Keywords
quantum invariants, Seifert manifolds, surgery, framed
links, modular categories, quantum groups
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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
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