Topology Seminar (Introductory Talk): Trisections and four-dimensional topology

Seminar | October 18 | 2-3 p.m. | 740 Evans Hall

 Jeffrey Meier, UGA

 Department of Mathematics

The notion of a trisection of a four-manifold was introduced by Gay and Kirby in 2012 and can be described as a decomposition of the four-manifold into three simple pieces. Trisections are the natural analogue in dimension four of Heegaard splittings of three-manifolds; in both cases, all of the topological complexity of the manifold is described by suitable collections of curves on surfaces. Since 2012, the theory of trisections has been rapidly developed and adapted to a number of new settings: most notably, the setting of knotted surfaces in four-manifolds.

In this talk, which will be accessible to any graduate student with some familiarity of low-dimensional manifolds (surfaces, Heegaard splittings, knots and links, etc.), I'll give an introduction to trisections and bridge trisections and describe the advances that have been made in the theory of trisections since its inception.