Date/Time Date(s) - 14/03/20253:30 pm - 4:30 pm
Speaker: Patrick Naylor (McMaster University) Research Area: Geometry & Topology
Location: Hamilton Hall, Room 305
Title: Cutting 4-manifolds into three equal pieces
Abstract: From the point of view of smooth manifolds, dimension four is quite unique— one striking illustration of this is the fact that R^n admits either one (if n is not equal to 4) or uncountably many (if n=4) smooth structures. There are many remaining fundamental questions about four dimensional topology, but one might hope to use lower dimensional tools to gain some insight.
One highly useful such tool is the notion of a Heegaard splitting: a decomposition of a 3—manifold into two “equal” pieces. In analogy with this decomposition, Gay and Kirby recently defined the notion of a trisection of a closed oriented 4—manifold: it is a similar decomposition, but into three equal pieces. Trisections provide a novel diagrammatic perspective on 4—manifolds, and have already been used to define new invariants and reprove fundamental results in gauge theory.
In this talk, I will describe these decompositions, variations thereof, and the interesting connections they have with surfaces, group theory, and other areas of mathematics.
Coffee will be served in the same room, HH 305 at 3:00pm. All are welcome.