Can Floer-theoretic invariants detect overtwisted contact structures?

GAUGE-TOPOLOGY-SYMPLECTIC

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February 15, 2019 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA
Speaker:

Cagatay Kutluhan - Buffalo

Abstract:

In joint work with Matic, Van Horn-Morris, and Wand, we seek an answer to this question. We define a refinement of the contact invariant in Heegaard Floer homology that takes values in Z_{\ge 0} \cup {\infty}, called (spectral) order. Among other things, we prove that overtwisted contact structures have zero order, whereas Stein fillable contact structures have infinite order. Furthermore, we show that a strictly increasing sequence of positive integers is realized as the order of a family of contact structures with vanishing Heegaard Floor contact invariant. After defining our contact invariant and discussing some of its key properties, I will talk about its computability and some problems that are content of work in progress.