# ag.algebraic geometry – Fundamental groups of primitive non-algebraic compact Kähler manifolds

Call a compact topological manifold $$M$$ primitive if there is no Serre fibration $$Mto B$$ where $$B$$ is a CW complex of dimension $$0.

Given a Kähler group $$G$$ does there exist a primitive non-algebraic compact Kähler manifold with $$pi_1=G$$?