The sheaf of the homology groups of the complex manifolds

Abstract

Let X be a connected complex n-dimensional manifold with fundemental group F_xneq{1}, H be the sheaf of the groups over X [7] and $Gamma$(X,H) be the group of the global sections of H over X. In this paper, the sheaf of the Homology groups is constructed by means of the homology grasps $H_x /N_x$ of the connected complex n-dimension manifold and given some characterizations. Finally, it is shown that if two connected complex manifolds are topologically equivalent, then their corresponding sheaves of the homology groups are isomorphic.