Tittel: Morse theory applied to the unitary group

Veileder: Markus Szymik

Sammendrag: There are many tools in mathematics which we can use to study manifolds. For example we might consider how functions on the manifold behave. By considering the critical points of functions from a manifold to the reals we can, through Morse theory, construct the manifold up to homotopy and even diffeomorphism. In this paper we introduce the basics of Morse theory as well as applying it to the the special case of the unitary group $U(n)$.