#### Volume 9, issue 4 (2009)

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Hyperbolic groups which fiber in infinitely many ways

### TaraLee Mecham and Antara Mukherjee

Algebraic & Geometric Topology 9 (2009) 2101–2120
##### Abstract

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

##### Keywords
hyperbolic groups, fibering
Primary: 20F65
Secondary: 51H99