Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 4 (2014), 2411-2430.
Stein fillable contact $3$–manifolds and positive open books of genus one
A –dimensional open book determines a closed, oriented –manifold and a contact structure on . The contact structure is Stein fillable if is positive, ie can be written as a product of right-handed Dehn twists. Work of Wendl implies that when has genus zero the converse holds, that is
On the other hand, results by Wand [Phd thesis (2010)] and by Baker, Etnyre and Van Horn–Morris [J. Differential Geom. 90 (2012) 1-80] imply the existence of counterexamples to the above implication with of arbitrary genus strictly greater than one. The main purpose of this paper is to prove the implication holds under the assumption that is a one-holed torus and is a Heegaard Floer –space.
Algebr. Geom. Topol., Volume 14, Number 4 (2014), 2411-2430.
Received: 10 April 2013
Revised: 5 January 2014
Accepted: 7 January 2014
First available in Project Euclid: 19 December 2017
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Lisca, Paolo. Stein fillable contact $3$–manifolds and positive open books of genus one. Algebr. Geom. Topol. 14 (2014), no. 4, 2411--2430. doi:10.2140/agt.2014.14.2411. https://projecteuclid.org/euclid.agt/1513715967