Weil-Petersson translation length and manifolds with many fibered fillings

Christopher J. Leininger (1) , Yair N. Minsky (2) , Juan Souto (3) , Samuel J. Taylor (4)

1 Rice University [Houston]
2 Department of Mathematics [Yale University]
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Temple University [Philadelphia]

We prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil-Petersson translation length contains a finite set of transverse and level closed curves, and drilling out this set of curves results in one of a finite number of cusped hyperbolic 3-manifolds. The number of manifolds in the finite list depends only on the bound for normalized translation length. We also prove a complementary result that explains the necessity of removing level curves by producing new estimates for the Weil-Petersson translation length of compositions of pseudo-Anosov mapping classes and arbitrary powers of a Dehn twist.

Mots clés: Weil–Petersson; Pseudo-Anosov; Fibered fillings

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Christopher J. Leininger, Yair N. Minsky, Juan Souto, Samuel J. Taylor. Weil-Petersson translation length and manifolds with many fibered fillings. Advances in Mathematics, In press, pp.107457. ⟨10.1016/j.aim.2020.107457⟩. ⟨hal-02998107⟩