Volume 14, issue 4 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Stein fillable contact $3$–manifolds and positive open books of genus one

Paolo Lisca

Algebraic & Geometric Topology 14 (2014) 2411–2430
[an error occurred while processing this directive]

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

ξ(S,h) Stein fillableh positive.

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.

Stein fillings, contact structures, open books
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57R57
Received: 10 April 2013
Revised: 5 January 2014
Accepted: 7 January 2014
Published: 28 August 2014
Paolo Lisca
Dipartimento di Matematica
Università di Pisa
Largo Bruno Pontecorvo 5
56121 Pisa