On the stable equivalence of open books in three-manifolds

Giroux, Emmanuel¹ ; Goodman, Noah²

¹ École Normale Supérieure de Lyon, 69364 Lyon cedex 07, France
² Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Geometry & topology, Tome 10 (2006) no. 1, pp. 97-114.

Résumé

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.

Détail

DOI : 10.2140/gt.2006.10.97

Keywords: open books, fibered links, plumbing, plane fields, contact structures

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