A group is said to algebraically fibre if it admits an epimorphism onto $\mathbb{Z}$ whose kernel satisfies suitable finiteness properties, such as finite generation or finite presentability.

The study of algebraic fibrations of hyperbolic groups has been a major theme in geometric group theory over the past two decades, motivated in part by the virtual fibering conjecture for odd-dimensional hyperbolic manifolds. Recently, Lafont, Minemyer, Sorcar, Stover, and Wells constructed, for every $d \geq 2$, a $d$-dimensional hyperbolic group admitting an algebraic fibration with finitely generated kernel.

We strengthen this result by showing that, for every $d \geq 3$, there exists a $d$-dimensional hyperbolic group admitting an algebraic fibration whose kernel is finitely presented.

Our construction combines right-angled Coxeter groups and Bestvina–Brady theory with a new collar-coning procedure inspired by a family of polytopes introduced by Löbell in the 1930s.

This is joint work with M. Migliorini and A. Ng.