Citation: Blanchet, Christian, et al. "Topological quantum field theories derived from the Kauffman bracket." Topology 34.4 (1995): 883-928.
Web: https://core.ac.uk/download/pdf/82219786.pdf
Tags: Physical, Foundational, Quantum-groups, TQFT
This early paper gives a formal mathematical realization of the SU(2) Witten TQFT. This construction is parallel to Reshetikhin-Turaev's. It is deeply skein-theoretic, in the sense that it works with the Kauffman bracket and skein relations intimately. This construction is equivalent to Reshetikhin-Turaev's. This equivalence is most obvious if one considers the Temperley-Lieb construction of MTCs, which is necessarily skein-theoretic.
The reason that some people prefer this approach is because, in the author's words, it is "purely topological".