Representations of Fundamental Groups of Compact Kahler Manifolds in Solvable Matrix Groups

Abstract

In the paper we prove a factorization theorem for representations of fundamental groups of compact Kähler manifolds ({\em Kähler groups}) into solvable matrix groups. We apply this result to prove that the universal covering of a compact Kähler manifold with a residually solvable fundamental group is holomorphically convex.