On the degree of a finite cover which fibers over circle

TL;DR

This paper establishes a lower bound on the degree of finite covers of hyperbolic 3-manifolds that fiber over the circle, relating it to volume, diameter, and new invariants.

Contribution

It introduces new invariants and provides a lower bound for the degree of covers of hyperbolic 3-manifolds fibering over the circle.

Findings

Lower bound depends on volume and diameter

Introduces new invariants for hyperbolic 3-manifolds

Connects cover degree with geometric properties

Abstract

We give a lower bound for the degree of a finite cover of a hyperbolic 3-manifold which fibers over the circle, in terms of volume, the diameter of the manifold and other new invariants.