Morse theory is a branch of differential topology. Equipping a manifold with a generic real-valued function allows one to use differential techniques to study fundamental topological properties of the manifold. This project will focus on applications of Morse theory to low-dimensional manifolds. Possible topics include

• the relationship with surface mapping class groups and
• Morse 2-functions on 3- and 4-manifolds.

Duration: 1 or 2 semesters