Group negative curvature for 3–manifolds with genuine laminations

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

References

Forward citations

Publication

Received: 5 August 1997

Revised: 9 May 1998

Published: 11 May 1998

Proposed: Jean-Pierre Otal

Seconded: Robion Kirby, Michael Freedman

Authors

David Gabai
California Institute of Technology Pasadena California 91125-0001 USA

William H Kazez
University of Georgia Athens Georgia 30602 USA

Volume 2, issue 1 (1998)

David Gabai and William H Kazez