Circular characteristics and fibrations of hyperbolic closed 3-manifolds

TL;DR

This paper establishes conditions based on the circular characteristic for hyperbolic 3-manifolds with non-zero first Betti number to fiber over the circle, providing methods to identify fibers via finite covers.

Contribution

It introduces a new approach using the circular characteristic to determine fibering over the circle in hyperbolic 3-manifolds, linking cohomology and Heegaard invariants.

Findings

Sufficient conditions for fibering over the circle in hyperbolic 3-manifolds.

Definition of the circular characteristic as an invariant.

Application of the circular characteristic to finite covers.

Abstract

This article provides sufficient conditions for a closed hyperbolic 3-manifold $M$ with non zero first Betti number to fiber over the circle, and to find a fiber in $M$. Those conditions are formulated in terms of the behavior the circular characteristic in finite regular covers of $M$. We define the circular characteristic as an invariant associated to a non trivial cohomology class $\alpha$ of $M$, using a Heegaard characteristic.