Geometry & Topology 2 (1998) 65–77

DOI: 10.2140/gt.1998.2.65

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: 20F32, 20F34, 57M07, 57M30, 57R30

References

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Publication

Received: 5 August 1997
Revised: 9 May 1998
Published: 11 May 1998
Proposed: Jean-Pierre Otal
Seconded: Robion Kirby, Michael Freedman

Authors