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

Paolo Lisca
2014 Algebraic and Geometric Topology  
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, 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 holds, that is On the other hand, results by Wand [24] and by Baker, Etnyre and Van Horn-Morris [3] imply the existence of counterexamples to ( * ) with S of arbitrary genus
more » ... itrary genus strictly greater than one. The main purpose of this paper is to prove ( * ) under the assumption that S is a one-holed torus and Y (S,h) is a Heegaard Floer L-space.
doi:10.2140/agt.2014.14.531 fatcat:dvlfikerwzftfdy64grksb42hi