Stein fillable contact 3–manifolds and positive open books of genus one

Lisca, Paolo¹

¹Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56121 Pisa, Italy

Algebraic and Geometric Topology, Tome 14 (2014) no. 4, pp. 2411-2430

Résumé

A 2–dimensional open book (S,h) determines a closed, oriented 3–manifold Y (S,h) and a contact structure ξ(S,h) on Y (S,h). The contact structure ξ(S,h) is Stein fillable if h is positive, ie h can be written as a product of right-handed Dehn twists. Work of Wendl implies that when S 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 S of arbitrary genus strictly greater than one. The main purpose of this paper is to prove the implication holds under the assumption that S is a one-holed torus and Y (S,h) is a Heegaard Floer L–space.

Détail

DOI : 10.2140/agt.2014.14.2411

Keywords: Stein fillings, contact structures, open books

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