Level N Teichm\"uller TQFT and Complex Chern-Simons Theory
  In this manuscript we review the construction of the Teichm\"{u}ller 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 $\rm{PSL}(2,\mathbb{C})$. 
J{\o}rgen Ellegaard Andersen and Simone Marzioni
math.GT math.QA