Geometry & Topology, Vol. 2 (1998) Paper no. 4, pages 65--77.

Group negative curvature for 3-manifolds with genuine laminations

David Gabai, William H. Kazez

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

AMS subject classification. Primary: 57M50. Secondary: 57R30, 57M07, 20F34, 20F32, 57M30.

DOI: 10.2140/gt.1998.2.65

E-print: arXiv:math.GT/9805152

Submitted to GT on 5 August 1997. (Revised 9 May 1998.) Paper published 11 May 1998.

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David Gabai, William H. Kazez
California Institute of Technology Pasadena, CA 91125-0001 USA
University of Georgia Athens, GA 30602, USA

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