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).
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