## A Heegaard Floer analog of algebraic torsion

Cagatay Kutluhan

University at Buffalo, The State University of New York; von Neumann Fellow, School of Mathematics

April 21, 2016

The dichotomy between overtwisted and tight contact structures has been central to the classification of contact structures in dimension 3. Ozsvath-Szabo's contact invariant in Heegaard Floer homology proved to be an efficient tool to distinguish tight contact structures from overtwisted ones. In this talk, I will motivate, define, and discuss some properties of a refinement of the contact invariant in Heegaard Floer homology. This is joint work with Grodana Matic, Jeremy Van Horn-Morris, and Andy Wand.