Tight contact structures and genus one fibered knots

Baldwin, John A¹

¹Department of Mathematics, Columbia University, New York, NY 10027

Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 701-735

Résumé

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]

Détail

DOI : 10.2140/agt.2007.7.701

Keywords: contact structure, Floer homology, knot, fibered, taut foliation, L-space

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