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Manuel Bärenz
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Is Turaev-Viro-Barrett-Westbury stronger than homotopy?

I've heard that Reshetikhin-Turaev (RT) is stronger than homotopy, and it can distinguish certain homotopy-equivalent, but non-homeomorphic Lens spaces (I think $L(7,1)$ and $L(7,2)$). Now the Turaev-Viro-Barrett-Westbury (TVBW) invariant for a spherical fusion category $\mathcal{C}$ is the Reshetikhin-Turaev invariant for $\mathcal{Z}(\mathcal{C})$, which is a restriction, so in principle, RT could be stronger than TVBW.

Are there calculations that show explicitly how TVBW is stronger than homotopy? What category do you have to use to achieve this?

Manuel Bärenz
  • 5.6k
  • 18
  • 49