Vol. 204, No. 1, 2002

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Heegaard splittings of Haken manifolds have bounded distance

Kevin Hartshorn

Vol. 204 (2002), No. 1, 61–75
Abstract

Given a Heegaard splitting and an incompressible surface S and a Heegaard splitting of an irreducible manifold, I shall use a generalization of Haken’s lemma proved by Kobayashi in order to define a pair of simple closed curves on the splitting surface such that each bounds a disc in one of the handlebodies of the splitting. By modifying the proof of Kobayashi’s lemma, I shall show that the sequence of boundary compressions used to isotope S places a bound on the distance between these two simple closed curves in the complex of curves. This will then place a bound on the distance of the Heegaard splitting.

Milestones
Received: 3 August 2000
Revised: 16 January 2001
Published: 1 May 2002
Authors
Kevin Hartshorn
Department of Mathematics
University of California, Davis
Davis, CA 95616