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arXiv:math/0111057 [math.GT]AbstractReferencesReviewsResources

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

Soren Kold Hansen

Published 2001-11-06Version 1

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.

Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-32.abs.html
Journal: Algebr. Geom. Topol. 1 (2001) 627-686
Categories: math.GT, math.QA
Subjects: 57M27, 17B37, 18D10, 57M25
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