In this talk, I will introduce the notion of a trisection of a group, and I'll explain how studying group trisections is equivalent to studying smooth structures on 4-manifolds.
The proof of this striking theorem, which is the main result of a recent eponymous paper by Abrams, Gay, and Kirby, involves a straightforward and beautiful synthesis of foundational theorems from the theories of 2-, 3-, and 4-dimensional manifolds. After presenting the proof, I will conclude by discussing connections to the Poincare Conjecture, Andrews-Curtis Conjecture, and knotted surface theory.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/TopologySeminar