Subfactors and 1+1-dimensional TQFTs

Details Subfactors and 1+1-dimensional TQFTs Subfactors and 1+1-dimensional TQFTs

2005-07-04

arxiv.org/abs/math/0507050v1

Int.J.Math.18:69-112,2007

Mathematics

Quantum Algebra

57 pages, 9 figures

Scientific paper

10.1142/S0129167X07003923

We construct a certain `cobordism category' ${\cal D}$ whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between (1+1-dimensional) unitary topological quantum field theories (TQFTs) defined on ${\cal D}$, on the one hand, and Jones' subfactor planar algebras, on the other.

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