Cohomological restrictions on Kahler groups

Abstract

The number of the relations of a Kahler group is bounded below by the number of the generators and some geometric invariants of the corresponding compact Kahler manifold, like the irregularity, the Albanese dimension and the Albanese genera. Appropriate functions of the aforementioned geometric invariants are shown to be lower bounds for the Betti numbers of the Kahler group within the range, determined by the Albanese dimension.