The stable homotopy classification of $(n-1)$-connected $(n+4)$-dimensional polyhedra with 2 torsion free homology

Abstract

In this paper, we study the stable homotopy types of ${\mathbf{F}}_{n(2)}^4$-polyhedra, i.e., $(n-1)$-connected, at most $(n+4)$-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable ${\mathbf{F}}_{n(2)}^4$-polyhedra. The proof relies on the matrix problem technique which was developed in the classification of representaions of algebras and applied to homotopy theory by Baues and Drozd.