WeilPetersson translation length and manifolds with many fibered fillings
Abstract
We prove that any mapping torus of a pseudoAnosov mapping class with bounded normalized WeilPetersson 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 3manifolds. 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 WeilPetersson translation length of compositions of pseudoAnosov mapping classes and arbitrary powers of a Dehn twist.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 DOI:
 10.48550/arXiv.1910.01169
 arXiv:
 arXiv:1910.01169
 Bibcode:
 2019arXiv191001169L
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Complex Variables;
 Mathematics  Differential Geometry
 EPrint:
 v2. Added references. v1. 49 pages, 9 figures