Quantum Trace and Dehn filling

I will briefly introduce the quantum trace map for hyperbolic links in the 3-sphere and its expectation value, computed by the $SL(2,C)$ Chern-Simons theory. I will argue, using the example of Dehn filling of the Whitehead link, that the operation of taking the expectation value of the quantum trace and Dehn filling commutes, at least, at the level of asymptotics of partition functions.