In this work a survey of restriction on the fundamental groups of Kahler manifolds and 4-manifold invariants of finitely presentable groups is given. In this context,
we prove that non-trivial free products of groups is not Kahler and we give some explicit calculations and number of properties of these invariants.
 
 

Keywords : Kahler Manifold, Fundamental Group, Eilenberg-Maclane Space,4-Manifold.