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Title:
Higher Quantum Teichmuller theory
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Abstract:
Given topological surface S with punctures and a split reductive group G with trivial center, e.g. PGL(n), we quantize the moduli space of flat G-connections on S. Namely, we define a non-commutative q-deformation A(G,S;q) of the algebra of regular functions on this moduli space -- it is a *-algebra. The mapping class group M(S) of S acts by its automorphisms. We define the following data:
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