The algebraic modular functor conjecture of Fock and Goncharov, that cutting a surface yields a canonical gluing isomorphism of the associated quantum algebras, is proven for type A_n (G = PGL(n+1)).
11Symplectic geometry of Teichm\"uller spaces for surfaces with ideal boundary.'' Communications in Mathematical Physics 405, no
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The algebraic modular functor conjecture in type $A_n$ quantum Teichm\"uller theory
The algebraic modular functor conjecture of Fock and Goncharov, that cutting a surface yields a canonical gluing isomorphism of the associated quantum algebras, is proven for type A_n (G = PGL(n+1)).