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

2014/06/30 by Mark Hagen, Mark F. Hagen, Daniel T. Wise · 1 citation
Computer Science · Mathematics · #Automorphism #Automorphism group #Combinatorics #Cube (algebra) #Cyclic group #Free group #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Hyperbolic function #Hyperbolic group #Hyperbolic manifold #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Physics #Pure mathematics #Rank (graph theory) #Word (group theory) #math.GR #semigroups and automata theory

paper · pdf · doi:10.1007/s00039-015-0314-y

36 pages, 11 figures. Version 2 contains minor corrections. Accepted to GAFA

arxiv created 2014/11/26 · openalex publication_date 2015/02/01 · arxiv updated 2016/05/27 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06

Abstract

Let Φ:F→ F be an automorphism of the finite-rank free group F. Suppose that G=F\rtimes_Φ\mathbb Z is word-hyperbolic. Then G acts freely and cocompactly on a CAT(0) cube complex.

Citations

• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
• Hyperbolic automorphisms of free groups
• Laminations, trees, and irreducible automorphisms of free groups
• Train Tracks and Automorphisms of Free Groups
• Finiteness properties of cubulated groups
• Cubulating malnormal amalgams
• Metric Spaces of Non-Positive Curvature
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning)

Cited by

• Some questions related to free-by-cyclic groups and tubular groups