## Geometry & Topology

### 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.

#### Article information

Source
Geom. Topol., Volume 10, Number 1 (2006), 97-114.

Dates
Accepted: 28 October 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799704

Digital Object Identifier
doi:10.2140/gt.2006.10.97

Mathematical Reviews number (MathSciNet)
MR2207791

Zentralblatt MATH identifier
1100.57013

#### Citation

Giroux, Emmanuel; Goodman, Noah. On the stable equivalence of open books in three-manifolds. Geom. Topol. 10 (2006), no. 1, 97--114. doi:10.2140/gt.2006.10.97. https://projecteuclid.org/euclid.gt/1513799704

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