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We investigate the conjectural relations between theReshetikhin-Turaev-Witten quantum SU(2) invariants and the volume of hyperbolic3-manifolds. Given a finite set of sufficiently large positive integers, say J,we construct examples of closed hyperbolic 3-manifolds with the same invariantsat all levels in J and different volume.

A NOTE ON QUANTUM 3-MANIFOLD INVARIANTS AND HYPERBOLIC VOLUME