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Turaev-Viro invariants as an extended TQFT III
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abstract
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.
Forward citations
Cited by 2 Pith papers
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Microscopic universal theory of symmetry-enriched topological quantum spin liquids
A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.
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Cochain valued TQFTs from nonsemisimple modular tensor categories
The authors construct a symmetric monoidal functor from admissible ribbon bordisms labeled by cochains over a modular tensor category to linear cochain complexes, extending the DGGPR TQFT and preserving homotopy equivalences.
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