A NOTE ON QUANTUM 3-MANIFOLD INVARIANTS AND HYPERBOLIC VOLUME

Abstract

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, such that τri(M) = 1, for i = 1,…, n.