Hyperbolic groups which fiber in infinitely many ways

Abstract

We construct examples of $CAT\left(0\right)$, free-by-cyclic, hyperbolic groups which fiber in infinitely many ways over $\mathbb{Z}$. 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 $CAT\left(0\right)$, hyperbolic, free-by-cyclic and can be mapped onto $\mathbb{Z}$ in infinitely many ways.