Level N Teichmüller TQFT and Complex Chern-Simons Theory

In this manuscript we review the construction of the Teichmüller TQFT in [AK1], upgrading it to a theory dependent on an extra odd integer $N$ using results developed in [AK3]. We also describe how this theory is related with quantum Chern--Simons Theory at level $N$ with gauge group $\rm{PSL}(2,\mathbb{C})$.

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