Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 18, pages 281--294.

(2+1)-dimensional topological quantum field theory with a Verlinde basis and Turaev-Viro-Ocneanu invariants of 3-manifolds

Nobuya Sato, Michihisa Wakui

Abstract. In this article, we discuss a (2+1)-dimensional topological quantum field theory, for short TQFT, with a Verlinde basis. As a conclusion of this general theory, we have a Dehn surgery formula. We show that Turaev-Viro-Ocneanu TQFT has a Verlinde basis. Several applications of this theorem are exposed. Based on Izumi's data of subfactors, we list several computations of Turaev-Viro-Ocneanu invariants for some 3-manifolds.

Keywords. Turaev-Viro-Ocneanu TQFT, Verlinde basis, Dehn surgery formula, tube algebra

AMS subject classification. Primary: 57R56, 81T45. Secondary: 46L37, 57M25, 57N10.

E-print: arXiv:math.QA/0210368

Submitted to GT on 30 November 2001. (Revised 7 March 2002.) Paper accepted 22 July 2002. Paper published 13 October 2002, with corrections to page 292 made 21 March 2003.

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Nobuya Sato, Michihisa Wakui
Department of Mathematics and Information Sciences
Osaka Prefecture University, Sakai, Osaka, 599-8531, Japan
and
Department of Mathematics, Osaka University
Toyonaka, Osaka 560-0043, Japan

Email: nobuya@mi.cias.osakafu-u.ac.jp, wakui@math.sci.osaka-u.ac.jp

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