Hyperbolic 5-manifolds that fiber over $S^1$

TL;DR

This paper constructs specific finite-volume hyperbolic 5-manifolds that fiber over the circle, including the smallest known example, and explores their implications for hyperbolic group theory.

Contribution

It presents the first examples of hyperbolic 5-manifolds that fiber over S^1, including the smallest known such manifold, and demonstrates a non-hyperbolic subgroup within a hyperbolic group.

Findings

Existence of finite-volume cusped hyperbolic 5-manifolds fibering over S^1

Construction of the smallest known hyperbolic 5-manifold

Identification of a finite type subgroup of a hyperbolic group that is not hyperbolic

Abstract

We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic.