Fibrations on Handlebodies

TL;DR

This paper demonstrates that certain 3-manifolds, including the genus 2 handlebody, admit uncountably many distinct fibrations over the circle with complex infinite-type fibers, expanding understanding of their topological structures.

Contribution

It constructs uncountably many fibrations with non-conjugate monodromies on handlebodies and other tame 3-manifolds, generalizing previous results.

Findings

Uncountably many fibrations on genus 2 handlebody.

Fibrations with fibers homeomorphic to Cantor tree surfaces.

Generalization to other tame 3-manifolds.

Abstract

We show that the open genus 2 handlebody admits uncountably-many fibrations over the circle with fiber homeomorphic to the Cantor tree surface with non-conjugate monodromies in the mapping class group. The construction generalizes to produce uncountably many fibrations of other tame 3-manifolds with infinite type fibers, including the blooming Cantor tree and many other types of surfaces.