Fibering rigidity of 3-manifolds with Torelli monodromy

TL;DR

This paper proves a uniqueness result for fibrations of hyperbolic 3-manifolds over the circle when the monodromy lies in the Torelli group, showing at most one such fibration exists up to isotopy.

Contribution

It establishes a rigidity theorem for fibrations with Torelli monodromy, demonstrating the uniqueness of such fibrations in hyperbolic 3-manifolds.

Findings

At most one fibration exists up to isotopy for hyperbolic 3-manifolds with Torelli monodromy.

Fibrations with Torelli monodromy are uniquely determined in hyperbolic 3-manifolds.

The result constrains the structure of fibrations in the Torelli setting.

Abstract

In this paper it is proven that there is at most one way, up to isotopy, in which a connected, hyperbolic, orientable 3-manifold can fiber over the circle with monodromy in the Torelli group.