Fundamental Group And Pluridifferentials On Compact Kahler Manifolds

A compact Kahler manifold X is shown to be simply connected if its 'symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic map f : X -> S between connected manifolds induces an isomorphism of fundamental groups if its smooth fibres are as above, and if X is Kahler.