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