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2007 Tight contact structures and genus one fibered knots
John A Baldwin
Algebr. Geom. Topol. 7(2): 701-735 (2007). DOI: 10.2140/agt.2007.7.701


We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual nonseparating curves in the once-punctured torus. Given such a product, we supply an algorithm to determine whether the corresponding contact structure is tight or overtwisted for all but a small family of reducible monodromies. We rely on Ozsváth–Szabó Heegaard Floer homology in our construction and, in particular, we completely identify the L–spaces with genus one, one boundary component, pseudo-Anosov open book decompositions. Lastly, we reveal a new infinite family of hyperbolic three-manifolds with no co-orientable taut foliations, extending the family discovered by Roberts, Shareshian, and Stein in [J. Amer. Math. Soc. 16 (2003) 639–679]


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John A Baldwin. "Tight contact structures and genus one fibered knots." Algebr. Geom. Topol. 7 (2) 701 - 735, 2007.


Received: 4 July 2006; Revised: 21 March 2007; Accepted: 21 March 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1202.57013
MathSciNet: MR2308961
Digital Object Identifier: 10.2140/agt.2007.7.701

Primary: 57M27, 57R17, 57R58
Secondary: 57R30

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.7 • No. 2 • 2007
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