An introduction to Kähler groups

A Kähler group is a finitely presented group that can be realized as fundamental group of a compact Kähler manifold. It is known that every finitely presented group can be realized as fundamental group of a compact real and even symplectic manifold of dimension greater equal than 4 and of a complex manifold of complex dimension greater equal than 2. In contrast, the question which groups are Kähler groups is surprisingly harder and there are large classes of examples for both, Kähler, and non-Kähler groups. This talk will give a brief introduction to the theory of Kähler manifolds and then discuss some basic examples and properties of Kähler groups. It is aimed at a general audience and no prior knowledge of the field will be required.