The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning)

2013/01/01 by Ian Agol · 5 citations
Computer Science · Arts and Humanities · Mathematics · #Cellular Automata and Applications #Art, Technology, and Culture #Mathematics #Conjecture #Mathematical economics #Calculus (dental) #Pure mathematics

paper · pdf · doi:10.4171/dm/421

openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/18

Abstract

We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are separable. A consequence is that closed hyperbolic 3-manifolds have finite-sheeted Haken covers, which resolves the virtual Haken question of Waldhausen and Thurston's virtual fibering question. An appendix to this paper by Agol, Groves, and Manning proves a generalization of the main result of [1].

Citations

• Completion of the Proof of the Geometrization Conjecture
• A topological characterisation of relatively hyperbolic groups
• On Irreducible 3-Manifolds Which are Sufficiently Large
• Virtually Haken fillings and semi-bundles
• Dehn filling in relatively hyperbolic groups
• Topology of finite graphs
• Ricci flow with surgery on three-manifolds

Cited by

• Hierarchically hyperbolic spaces, I: Curve complexes for cubical groups
• On growth rate and contact homology
• Cubulating hyperbolic free-by-cyclic groups: the general case
• Farrell–Jones via Dehn fillings
• Tensor Product Decompositions of II1 Factors Arising from Extensions of Amalgamated Free Product Groups
• Congruence subgroup [wikipedia]

Related

• The virtual Haken conjecture
• Specializing cubulated relatively hyperbolic groups
• A new proof of the virtual Haken conjecture
• Some virtually special hyperbolic 3-manifold groups
• Hyperbolic Manifolds and Discrete Groups