Embeddings of lens spaces and rational homology balls in complex projective space

Geometry Topology Working Seminar
Friday, September 23, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Agniva Roy – Georgia Tech
John Etnyre

Given a symplectic 4 manifold and a contact 3 manifold, it is natural to ask whether the latter embeds in the former as a contact type hypersurface. We explore this question for CP^2 and lens spaces. In this talk, we will consider the background necessary for an approach to this problem. Specifically, we will survey some essential notions and terminology related to low-dimensional contact and symplectic topology. These will involve Dehn surgery, tightness, overtwistedness, concave and convex symplectic fillings, and open book decompositions. We will also look at some results about these and mention some research trends.