Kitaev's Lattice Model and Turaev-Viro TQFTs
  In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Turaev-Viro theory on a surface with boundary. 
Benjamin Balsam, Alexander Kirillov Jr
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