## Geometry & Topology

### Group negative curvature for 3–manifolds with genuine laminations

#### 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.

#### Article information

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

Dates
Revised: 9 May 1998
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882902

Digital Object Identifier
doi:10.2140/gt.1998.2.65

Mathematical Reviews number (MathSciNet)
MR1619168

Zentralblatt MATH identifier
0905.57011

#### Citation

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. https://projecteuclid.org/euclid.gt/1513882902

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