Symplectic trisections and connected sum decompositions

Geometry Topology Seminar
Monday, April 17, 2023 - 4:30pm for 1 hour (actually 50 minutes)
Skiles 006
Peter Lambert-Cole – University of Georgia
Austin Christian

This talk will have two parts.  The first half will describe how to construct symplectic structures on trisected 4-manifolds. This construction is inspired by projective complex geometry and completely characterizes symplectic 4-manifolds among all smooth 4-manifolds.  The second half will address a curious phenomenon: symplectic 4-manifolds appear to not admit any interesting connected sum decompositions.  One potential explanation is that every embedded 3-sphere can be made contact-type.  I will outline some strategies to prove this from a trisections perspective, describe some of the obstructions, and give evidence that these obstructions may be overcome.