On Chen–Yang’s volume conjecture for various quantum invariants

Abstract

Chen and Yang extended the volume conjecture of quantum ${\mathcal U}_q(sl_2)$ invariant by putting $q$ = exp$(4\pi i/r)$ instead of exp$(2\pi i/r)$/ for odd $r$ and they fond that the conjecture holds not only for complements of knots but also for various hyperbolic three-manifolds. Here we show numerical verifications of several variations of their conjecture.