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ThiKu
ThiKu
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In the paper Sato-WajuiWakui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results is that the generalized $E_6$ subfactor for $\mathbb{Z}/p$ distinguishes the lens spaces $L(p,1)$ and $L(p,2)$ for $p=3,5$, and they conjecture (or at least raise the question) of whether this holds for $p=7$.

I am wondering if any progress has been made on this question since this paper appeared?

In the paper Sato-Wajui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results is that the generalized $E_6$ subfactor for $\mathbb{Z}/p$ distinguishes the lens spaces $L(p,1)$ and $L(p,2)$ for $p=3,5$, and they conjecture (or at least raise the question) of whether this holds for $p=7$.

I am wondering if any progress has been made on this question since this paper appeared?

In the paper Sato-Wakui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results is that the generalized $E_6$ subfactor for $\mathbb{Z}/p$ distinguishes the lens spaces $L(p,1)$ and $L(p,2)$ for $p=3,5$, and they conjecture (or at least raise the question) of whether this holds for $p=7$.

I am wondering if any progress has been made on this question since this paper appeared?

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Chris Schommer-Pries
Chris Schommer-Pries
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Does the Turaev-Viro theory for the generalized $E_6$ subfactor for $\mathbb{Z}/7$ distinguish $L(7,1)$ and $L(7,2)$?

In the paper Sato-Wajui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results is that the generalized $E_6$ subfactor for $\mathbb{Z}/p$ distinguishes the lens spaces $L(p,1)$ and $L(p,2)$ for $p=3,5$, and they conjecture (or at least raise the question) of whether this holds for $p=7$.

I am wondering if any progress has been made on this question since this paper appeared?