  This paper concerns with a rigidity of core geodesics in hyperbolic Dehn
fillings. For instance, for an $n$-cusped hyperbolic $3$-manifold $M$ having
non-symmetric cusp shapes, we show any Dehn filling of $M$ with sufficiently
large coefficient is uniquely determined by the product of the holonomies of
its core geodesics. We also explore various implications of the main results.
An appendix by I. Agol provides an alternative geometric proof of one of the
corollaries of our main arguments.
