(2+1)-dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3-manifold invariants

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dc.creatorKawahigashi, Yasuyuki
dc.creatorSato, Nobuya
dc.creatorWakui, Michihisa
dc.date2002-08-30
dc.date.accessioned2026-07-07T04:50:28Z
dc.date.available2026-07-07T04:50:28Z
dc.descriptionIn this paper, we establish the general theory of (2+1)-dimensional topological quantum field theory (in short, TQFT) with a Verlinde basis. It is a consequence that we have a Dehn surgery formula for 3-manifold invariants for this kind of TQFT's. We will show that Turaev-Viro-Ocneanu unitary TQFT's obtained from subfactors satisfy the axioms of TQFT's with Verlinde bases. Hence, in a Turaev-Viro-Ocneanu TQFT, we have a Dehn surgery formula for 3-manifolds. It turns out that this Dehn surgery formula is nothing but the formula of the Reshetikhin-Turaev invariant constructed from a tube system, which is a modular category corresponding to the quantum double construction of a C^*-tensor category. In the forthcoming paper, we will exbit computations of Turaev-Viro-Ocneanu invariants for several ``basic 3-manifolds ''. In Appendix, we discuss the relationship between the system of M_{infinity}-M_{infinity} bimodules arising from the asymptotic inclusion M V M^{op} subset M_{infinity} constructed from N subset M and the tube system obtained from a subfactor N subset M.
dc.description37 pages, 36 figures
dc.identifierhttps://arxiv.org/abs/math/0208238
dc.identifierhttp://arxiv.org/abs/math/0208238
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64804
dc.subjectOperator Algebras
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject46L37;57N10
dc.title(2+1)-dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3-manifold invariants
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