Alladi Ramakrishnan Hall

Contact Structures and Heegaard Floer Homology

Dheeraj Kulkarni

ISI, Kolkata

There is a dichotomy between contact structures-- tight and overtwisted. Classification of overtwisted contact structures up to isotopy, due to Eliashberg, is well-known. There have been few results towards classification of tight contact structures. However, in general, given a contact structure it is difficult to know whether it is tight or not.

In this talk, we focus on the role of certain element, called as contact invariant, of Heegaard Floer homology group associated with a given contact structure in understanding tightness. We discuss success and limitations of contact invariant in detecting tightness of contact structures. In this direction, I will present a recent result from joint work with James Conway and Amey Kaloti.
We will briefly survey the relevant notions from Contact Topology and Heegaard Floer Homology in the first half of the talk.