On The Cohomology Groups Of Complex analytic Manifolds

Abstract

Let X be a connected complex analytic manifold of dimension n with fundamental group 7^ {1}’ xgX. Let H be the sheaf of the fundamental groups över X, [H.H] <= H be the commutator subsheaf, Q be the sheaf of Abelian groups [1 ] determined by [H,H ] över X and A be the Restricted sheaf of germs of holomorphic functions on X defined in [4 ]. It is shown, in this paper, that; The Cohomology group H®(X,Q) of the structure sheaf Q of X is isomorphic to the Cohomology gorup H®(X,A) of the structure restricted sheaf A of X. Moreover, the Co­ homology group HP(X,Q) of the structure sheaf Q of X and the Ğech Cohomology group stnıcture sheaf Q of equal to zero, for p 1.