Criteria for virtual fibering

2007/07/31 by Ian Agol · 2 citations
Mathematics · #Computer science #Corollary #Cover (algebra) #Fibered knot #Foliation (geology) #Fundamental group #Geology #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Mathematics #Property (philosophy) #Pure mathematics #Quadratic equation #Space (punctuation) #math.GR #math.GT #msc:57M10 #msc:57R22

paper · pdf · doi:10.1112/jtopol/jtn003

17 pages, 3 figures; new theorem 7.2; to appear in Journal of Topology

arxiv created 2008/02/24 · openalex publication_date 2008/04/01 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that an irreducible 3-manifold with fundamental group that satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber dodecahedral space and the Bianchi groups. Moreover, we show that a taut-sutured compression body has a finite-sheeted cover with a depth one taut-oriented foliation.

Citations

• Virtual betti numbers of symmetric spaces
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Subgroups of Surface Groups are Almost Geometric
• The asymptotic behaviour of Heegaard genus

Cited by

• Some questions related to free-by-cyclic groups and tubular groups
• Virtually fibered conjecture [wikipedia]

Related

• The virtual fibering theorem for 3-manifolds
• Some virtually special hyperbolic 3-manifold groups
• The virtual Haken conjecture
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning)
• On some of the residual properties of finitely generated nilpotent\n groups