FOUR MANIFOLDS AND KIRBY CALCULUS
The course introduces modern techniques of differential topology through handle calculus, and pays special attention to the description of 4-dimensional manifolds. We also show how to manipulate diagrams representing 4-manifolds. Smooth invariants of 3- and 4-manifolds (Heegaard Floer invariants and Seiberg-Witten invariants) will be also discussed.
By the end of the course, students are enabled to do independent study and research in fields touching on the topics of the course, and how to use these methods to solve specific problems. In addition, they develop some special expertise in the topics covered, which they can use efficiently in other mathematical fields, and in applications, as well. They also learn how the topic of the course is interconnected to various other fields in mathematics, and in science, in general.