Topology Seminar (Main Talk): Bridge trisections, complex curves, and exotic four-manifolds

Seminar | October 18 | 4-5 p.m. | 3 Evans Hall

 Jeffrey Meier, UGA

 Department of Mathematics

The theory of knotted surfaces in four-manifolds (the natural analogue of knot theory to dimension four) is one of the richest and least-explored domains of low-dimensional topology. In this talk, I'll outline some of the most intriguing open problems in this area, and I'll discuss a new approach to four-dimensional knot theory that is inspired by the theory of trisections, which was introduced by Gay and Kirby in 2012. Particular focus will be placed on the setting of complex curves in the simplest complex manifolds: \(\mathbb {CP}^2\) and \(S^2\times S^2\). In this setting, the theory of bridge trisections has produced surprisingly beautiful pictures, which intriguing implications to the study of exotic smooth structures on (complex) four-manifolds.