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moduli of representations (Betti moduli), moduli of Higgs bundles (Dolbeault moduli), moduli of connections (de Rham moduli space), moduli of principal bundles (Čech moduli space), moduli of polygons, moduli of geometric structures, spin networks, skein theory, A-polynomial, higher Teichmüller theory
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Deriving the Hilbert spaces for Chern-Simons TQFTs with complex gauge group
The quantization procedure is proposed by Gukov by using A-polynomials
http://arxiv.org/abs/hep-th/0306165
This quantization is shown to be true for $SL(2,\mathbb{C})$ character variety of hyperboli …