Spectral order invariant and obstruction to Stein fillability

Abstract: In this joint work with Cagatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. 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. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsváth-Szabó contact class.

Mathematics

Audience: researchers in the topic

Regensburg low-dimensional geometry and topology seminar