Cubulating hyperbolic free-by-cyclic groups: the general case

By Mark F. Hagen, Daniel T. Wise. 2014

79 citations recorded by the source corpus.

Let $${\Phi\colon F\rightarrow F}$$Φ:F→F be an automorphism of the finite-rank free group F. Suppose that $${G=F\rtimes_\Phi\mathbb{Z}}$$G=F⋊ΦZ is word-hyperbolic. Then G acts freely and cocompactly on a CAT(0) cube complex.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/99084f9919287047e7da845cd41f11fa5952e6a3

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In Computational Theory and Mathematics

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Citations in the corpus

Hierarchically hyperbolic spaces I: curve complexes for cubical groups (2014, background): “Other examples of cubical groups include: groups satisfying sufficiently strong small-cancellation conditions [Wis04]; many 3–manifold groups, including all hyperbolic ones [KM09, BW13, Wis] and some graph manifold groups [HP13]; hyperbolic free-by-Z groups [HW14]; etc.”
Hierarchically hyperbolic spaces II: Combination theorems and the distance formula (2015, result): “Indeed, by combining results in [HW15] and [Ago13], one nds that G acts freely, cocompactly, and hence virtually co-specially on a CAT(0) cube complex, which therefore contains a G-invariant factor system in the sense of [BHS14] and is hence a hierarchically hyperbolic group; the construction in [BH”