ON TWO APPROACHES TO 3-DIMENSIONAL TQFTS

By Vladimir Turaev, Alexis Virelizier. 2010

76 citations recorded by the source corpus.

We prove that |M|C = �Z(C)(M) for any closed oriented 3-manifold M and for any spherical fusion category C of non-zero dimension. Here |M|C is the Turaev-Viro-Barrett-Westbury state sum invariant of M derived from C, Z(C) is the Drinfeld-Joyal-Street center of C, andZ(C)(M) is the Reshetikhin- Turaev surgery invariant of M derived from Z(C).

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b84e8e4681040e58a2ee6f5c0c2c196ea9531bc8

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In Discrete Mathematics and Combinatorics

1. Kevin Walker
2. Zhenghan Wang

In Geometry and Topology

1. Kevin Walker
2. Zhenghan Wang
3. B. Yoshida
4. Ryan Thorngren
5. Ashvin Vishwanath
6. A. Kapustin
7. K. Costello

Citations in the corpus

• (3+1)-TQFTs and topological insulators (2011, methodology): “wo mathematical theorems: The quantum double Z(C) of a unitary fusion category C is always modular, and the Turaev-Viro TQFT based on C is equivalent to the Reshetikhin-Turaev TQFT based on Z(C) [Mue][TVi][BenK]. Therefore, Levin-Wen model is a Hamiltonian 14 KEVINWALKERANDZHENGHANWANG realization o”