Kitaev's Lattice Model and Turaev-Viro TQFTs

Understand

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.