## Topology Seminar (Introductory Talk): Heegaard Floer homology in Contact Geometry

Seminar | February 8 | 2:10-3 p.m. | 736 Evans Hall

James Conway, UC Berkeley

Department of Mathematics

Contact 3-manifolds come in two main flavours: tight and overtwisted. Suppose we are given a contact 3-manifold $(M, \xi )$: what tools can we use to show that it is tight? I will describe two tools – Heegaard Floer homology and open book decompositions – and how they have been used (together) to give contact invariants to help answer this question. In particular, we will see how Heegaard Floer invariants interact nicely with surgery on Legendrian knots.

hongbins@berkeley.edu