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

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

2001-11-06

arxiv.org/abs/math/0111057v1

Algebr. Geom. Topol. 1 (2001) 627-686

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-32.abs.html

Scientific paper

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.

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