[Topology and Geometry Seminar] “Trisections of 4-manifolds” by Dr Dale Koenig
The seminar aims to introduce research topics in topology, geometry and its interactions with other sciences. Anyone interested in mathematics is welcome to attend.
This week, Dr Dale Koenig (postdoc in the Tsvietkova Unit) will speak on "Trisections of 4-manifolds".
Abstract: I will give an introduction to the theory of trisections of 4-manifolds, developed by David Gay and Robion Kirby. This theory began with their 2012 preprint and has since blossomed into a popular field of study. Just as Heegaard splittings of 3-manifolds give a way to break a 3-manifold into two pieces and represent the manifold by two sets of curves on a surface, we can break a 4-manifold into three pieces and represent the manifold by three sets of curves on a surface. I will discuss the definition of a trisection, the notion of stabilization for trisections, constructing trisection diagrams, and the classification of low genus trisections.