On the asymptotic expansion for the relative Reshetikhin-Turaev invariants of fundamental shadow link pairs

Abstract

We verify the leading order term in the asymptotic expansion conjecture of the relative Reshetikhin-Turaev invariants proposed in [56] for all pairs (M, L) satisfying the properties that M L is homeomorphic to some fundamental shadow link complement and the 3-manifold M is obtained by doing rational Dehn filling on some boundary components of the fundamental shadow link complement, under the assumptions that the denominator of the surgery coefficients are odd and the cone angles are sufficiently small. In particular, the asymptotics of the invariants captures the complex volume and the twisted Reidemeister torsion of the manifold M L associated with the hyperbolic cone structure determined by the sequence of colorings of the framed link L.