# Surfaces in four-manifolds

## Location

383N

Monday, October 17, 2022 4:00 PM

András Stipsicz, Alfréd Rényi Institute of Mathematics

The genus function (associating the minimal genus representative to a homology class) of a closed four-manifold can measure exotic behaviour in four-dimensional topology.

We know this function only in a handful of cases; in the lecture I will describe some of these.

The notion extends to four-manifolds with boundary by considering slice surfaces for knots in the boundary; the examination of that function leads us to a result concerning our chances of finding exotic four-spheres.