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arXiv · 1304.1299

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

Paolo Lisca
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Abstract

A two-dimensional open book (S,h) determines a closed, oriented three-manifold Y(S,h) and a contact structure C(S,h) on Y(S,h). The contact structure C(S,h) is Stein fillable if h is positive, i.e. h can be written as a product of right-handed Dehn twists. Work of Wendl implies that when S has genus zero the converse statement holds, that is if C(S,h) is Stein fillable then h is positive. On the other hand, results by Wand and by Baker, Etnyre and Van Horn-Morris imply the existence of counterexamples to the converse statement with S of arbitrary genus strictly greater than one. The main purpose of this paper is to prove the converse statement under the assumption that S is a one-holed torus and Y(S,h) is a Heegaard Floer L-space.

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Paolo Lisca. 2013-04-04. Stein fillable contact 3-manifolds and positive open books of genus one. https://doi.org/10.2140/agt.2014.14.2411

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