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

Nobuya Sato and Michihisa Wakui

Geometry & Topology Monographs 4 (2002) 281–294

DOI: 10.2140/gtm.2002.4.281

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

Mathematical Subject Classification

Primary: 57R56, 81T45

Secondary: 46L37, 57M25, 57N10

References
Publication

Received: 30 November 2001
Revised: 7 March 2002
Accepted: 22 July 2002
Published: 13 October 2002
Corrected: 21 March 2003 (corrections to page 292)

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