Filtering the Heegaard Floer contact invariant

Cagatay Kutluhan; Gordana Matic; Jeremy Van Horn-Morris; Andy Wand

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arXiv · 1603.02673

Filtering the Heegaard Floer contact invariant

Cagatay Kutluhan·Gordana Matic·Jeremy Van Horn-Morris·Andy Wand

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Abstract

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set $\mathbb{Z}_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, $\infty$ for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. As an application, we obstruct Stein fillability on contact 3-manifolds with non-vanishing Ozsv\'ath-Szab\'o contact class.

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Cagatay Kutluhan, Gordana Matic, Jeremy Van Horn-Morris, Andy Wand. 2016-03-08. Filtering the Heegaard Floer contact invariant. https://arxiv.org/abs/1603.02673

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