Turaev-Viro invariants as an extended TQFT III

Details Turaev-Viro invariants as an extended TQFT III Turaev-Viro invariants as an extended TQFT III

2010-12-02

arxiv.org/abs/1012.0560v2

Mathematics

Quantum Algebra

19 pages, many figures. Added explanation of equivalence of theories for extended 3-manifolds and added description of TV theo

Scientific paper

In the third paper in this series, we examine the Reshetikhin-Turaev and Turaev-Viro TQFTs at the level of surfaces. In particular, we show that for a closed surface $\Sigma$, $Z_{TV, \mathcal{C}}(\Sigma) \cong Z_{RT, Z(\C)}(\Sigma)$, thus extending the equality of 3-manifold invariants proved in an earlier paper to an equivalence of TQFTs. We also describe how to compute Turaev-Viro state sums for 3-manifolds with embedded ribbon graphs.

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