On the sheaf $H_n$ of higher homotopy groups as an Abelian covering space

Abstract

Let X be a connected and locally path connected topological space. Constructing the sheaf $H_n$ of higher homotopy groups on X, its some characterizations are examined. Also, it is shown that $H_n$ is a regular covering space asa sheaf of abelian groups. Finally, it is given "General Lifting Theorem" for the sheaf $H_n$ and constructing the Quotient Sheaf Q for any group subsheaf $H_n$of the sheaf $H_n$ ,it is shown that $Q_{H_n}$ is a covering space as a sheaf of abelian groups.