A knot-theoretic tour of dimension four

Abstract

These notes follow a lecture series at the "Singularities and low dimensional topology" winter school at the Rényi Institute in January 2023, with a target audience of graduate students in singularity theory and low-dimensional topology. The lectures discuss the basics of four-dimensional manifold topology, connecting this rich subject to knot theory on one side and to contact, symplectic, and complex geometry (through Stein surfaces) on the other side of the spectrum.

30 pages, 21 figures