#### Volume 2, issue 1 (1998)

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Group negative curvature for 3–manifolds with genuine laminations

### David Gabai and William H Kazez

Geometry & Topology 2 (1998) 65–77
 arXiv: math.GT/9805152
##### 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.

##### Keywords
lamination, essential lamination, genuine lamination, group negatively curved, word hyperbolic
##### Mathematical Subject Classification
Primary: 57M50
Secondary: 57R30, 57M07, 20F34, 20F32, 57M30