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he classical Kauffman bracket is an invariant of knots in space, closely related to the Jones polynomial. Witten's interpretation of the Jones polynomial in the framework of a topological quantum field theory leads to a generalization of Kauffman brackets to knots drawn on a surface. I will discuss invariants of these generalized Kauffman brackets, as well as the construction of a wide family of Kauffman brackets that realizes all possible invariants and greatly generalizes the original Witten-Reshetikhin-Turaev example. This is joint work with Helen Wong.