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On picture $$(2+1)$$-TQFTs. (English) Zbl 1168.81024
Lin, Kevin (ed.) et al., Topology and physics. Proceedings of the Nankai international conference in memory of Xiao-Song Lin, Tianjin, China, July 27–31, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-281-910-9/hbk). Nankai Tracts in Mathematics 12, 19-106 (2008).
From the introduction: The content of each section is as follows. In Sections 2, 3, we treat diagram TQFTs for closed manifolds. In Sections 4. 5, 7.1. we handle boundaries. In Sections 7, 9, 8, we cover the related Jones-Kauffman TQFTs, and the Witten-Reshetikhin-Turaev SU(2)-TQFTs which have anomaly, and non-trivial Frobenius-Schur indicators, respectively. In Section 10, we first prove the uniqueness of TQFTs based on Jones-Wenzl projectors, and then classify them according to the Kauffman variable $$A$$. A theory $$V$$ or $${\mathcal D}(V)$$ is unitary if the vector spaces $$V$$ have natural positive definite Hermitian structures. Only unitary theories will have physical relevance so we decide for each theory if it is unitary.
For the entire collection see [Zbl 1154.82001].

##### MSC:
 81T45 Topological field theories in quantum mechanics 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81V70 Many-body theory; quantum Hall effect 57M27 Invariants of knots and $$3$$-manifolds (MSC2010)