For a closed, oriented 3-manifold M and an integer r > 0, let τr(M) denote the SU(2) Reshetikhin-Turaev-Witten invariant of M , at level r. We show that for every n > 0, and for r1, . . . , rn > 0 sufficiently large integers, there exist infinitely many non-homeomorphic hyperbolic 3-manifolds M , all of which have different hyperbolic volume, and such that… (More)