Geometry & Topology

Group negative curvature for 3–manifolds with genuine laminations

David Gabai and William H Kazez

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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.

Article information

Geom. Topol., Volume 2, Number 1 (1998), 65-77.

Received: 5 August 1997
Revised: 9 May 1998
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57R30: Foliations; geometric theory 57M07: Topological methods in group theory 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx] 20F32 57M30: Wild knots and surfaces, etc., wild embeddings

lamination essential lamination genuine lamination group negatively curved word hyperbolic


Gabai, David; Kazez, William H. Group negative curvature for 3–manifolds with genuine laminations. Geom. Topol. 2 (1998), no. 1, 65--77. doi:10.2140/gt.1998.2.65.

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