Hyperbolic Groups Which Fiber in Infinitely Many Ways

TL;DR

This paper constructs specific hyperbolic groups that are free-by-cyclic and can fiber over Z in infinitely many ways, expanding understanding of group structures with multiple fibrations.

Contribution

It introduces a novel construction method for hyperbolic free-by-cyclic groups with infinitely many fibrations over Z.

Findings

Constructed examples of hyperbolic free-by-cyclic groups with multiple fibrations

Demonstrated the groups can be mapped onto Z in infinitely many ways

Extended the class of known hyperbolic groups with complex fibering properties

Abstract

We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented graphs. The fundamental groups of the resulting complexes are hyperbolic, free-by-cyclic and can be mapped onto Z in infinitely many ways.