On the stable equivalence of open books in three-manifolds

Abstract

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous. Since this condition is automatically fulfilled in an integral homology sphere, the theorem implies a conjecture of J Harer, namely, that any fibered link in the three-sphere can be obtained from the unknot by a sequence of plumbings and deplumbings of Hopf bands. The proof presented here involves contact geometry in an essential way.

This is the version published by Geometry & Topology on 4 March 2006

References in corpus (2)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Classes d'homotopie de champs de vecteurs Morse-Smale sans singularité sur les fibrés de Seifert

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