Stable homotopy classification of A_n^4-polyhedra with 2-torsion free homology

We study the stable homotopy types of F_n^4(2)-polyhedra, i.e.,(n- 1)-connected, at most(n+ 4)-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable F_n^4(2)-polyhedra. The proof relies on the matrix problem technique which was developed in the classification of representations of algebras and applied to homotopy theory by Baues and Drozd(1999, 2001, 2004).