Classification of hyperbolic Dehn fillings I

Abstract Let be a 2‐cusped hyperbolic 3‐manifold. By the work of Thurston, the product of the derivatives of the holonomies of core geodesics of each Dehn filling of is an invariant of it. In this paper, we classify Dehn fillings of with sufficiently large coefficients using this invariant. Further, for any given two Dehn fillings of (with sufficiently larger coefficients), if their aforementioned invariants are the same, it is shown their complex volumes are the same as well.