Algebraic fibrings of a hyperbolic $7$-manifold

TL;DR

This paper demonstrates the existence of a finite-volume hyperbolic 7-manifold that algebraically fibers with a kernel of specific finiteness properties, extending previous constructions.

Contribution

It constructs a new hyperbolic 7-manifold that algebraically fibers with a finitely presented kernel of type FP(Q), building on prior work by Italiano--Martelli--Migliorini.

Findings

Existence of a hyperbolic 7-manifold with algebraic fibering.

The manifold is a finite cover of a previously known example.

The kernel of the fibering map has type FP(Q).

Abstract

We show there is a finite-volume, hyperbolic $7$-manifold that algebraically fibres with finitely presented kernel of type $\mathtt{FP}(\mathbb Q)$. This manifold is a finite cover of the one constructed by Italiano--Martelli--Migliorini.