Group negative curvature for 3–manifolds with genuine laminations

1998/05/11 by David Gabai, William H. Kazez, William H Kazez · 29 citations
Mathematics · #Analytic and geometric function theory #Corollary #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group (periodic table) #Group action #Isoperimetric inequality #Lamination #Negative curvature #math.GT #msc:20F32 #msc:20F34 #msc:57M07 #msc:57M30 #msc:57M50 #msc:57R30

paper · pdf · doi:10.2140/gt.1998.2.65

published in Geometry & Topology 2(1), 65-77 (Mathematical Sciences Publishers) · 13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper4.abs.html

arxiv created 1998/05/11 · openalex publication_date 1998/05/11 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that if a closed atoroidal 3-manifold M contains a genuine lamination, then it is group negatively curved in the sense of Gromov. Specifically, we exploit the structure of the non-product complementary regions of the genuine lamination and then apply the first author's Ubiquity Theorem to show that M satisfies a linear isoperimetric inequality.

Citations

• On the geometry and dynamics of diffeomorphisms of surfaces
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Theorie der Normalflächen: Ein Isotopiekriterium für den Kreisknoten
• Hyperbolic Groups