Weil–Petersson translation length and manifolds with many fibered fillings

We prove that any mapping torus of a pseudo-Anosov class with bounded normalized Weil–Petersson translation length contains finite set transverse and level closed curves the property drilling out this results in one number cusped hyperbolic 3–manifolds. Moreover, resulting manifolds depends only on bound for length. This gives analog theorem Farb–Leininger–Margalit [9] about Teichmüller also complementary result explains necessity removing by producing new estimates compositions classes arbitrary powers Dehn twist.