# Handlebody Bundles and Polytopes

## TL;DR

This paper constructs specific fibered three-manifolds with multiple fibered faces where all monodromies extend to handlebodies, advancing understanding of the relationship between fibered structures and handlebody extensions.

## Contribution

It introduces new examples of fibered three-manifolds with monodromies extending to handlebodies, highlighting novel geometric and topological properties.

## Key findings

- Existence of fibered three-manifolds with first Betti number ≥ 2
- All fibered faces have monodromies extending to handlebodies
- Provides explicit constructions of such manifolds

## Abstract

We construct examples of fibered three-manifolds with first Betti number at least 2 and with fibered faces all of whose monodromies extend to a handlebody.