On the stable equivalence of open books in three-manifolds

Details On the stable equivalence of open books in three-manifolds On the stable equivalence of open books in three-manifolds

2005-09-23

arxiv.org/abs/math/0509555v2

Geom. Topol. 10 (2006) 97-114

Mathematics

Geometric Topology

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

Scientific paper

10.2140/gt.2006.10.97

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.

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